Anca Molnos
email: anca.molnos@cea.fr

Warody Lombardi

Diego Puschini

Julien Mottin

Suzanne Lesecq

Arnaud Tonda

Energy Management via PI Control for Data Parallel Applications with Throughput Constraints

This paper presents a new proportional-integral (PI) controller that sets the operating point of computing tiles in a system on chip (SoC). We address data-parallel applications with throughput constraints. The controller settings are investigated for application configurations with different QoS levels and different buffer sizes. The control method is evaluated on a test chip with four tiles executing a realistic HMAX object recognition application. Experimental results suggest that the proposed controller outperforms the state-of-the-art results: it attains, on average, 25% less number of frequency switches and has slightly higher energy savings. The reduction in number of frequency switches is important because it decreases the involved overhead. In addition, the PI controller meets the throughput constraint in cases where other approaches fail.

I. INTRODUCTION

Reducing energy consumption in embedded computing systems is still a challenge, despite many recent advances on the subject. Recent hardware platforms integrate multiple processor cores on a chip and support operating point switching, e.g., dynamic frequency and/or voltage scaling (DVFS) at the level of processor cores [START_REF] Panades | A fine-grain variation-aware dynamic Vddhopping AVFS architecture on a 32 nm GALS MPSoC[END_REF], clusters [START_REF] Melpignano | Platform 2012, a many-core computing accelerator for embedded socs: performance evaluation of visual analytics applications[END_REF] or entire chip [START_REF] Varghese | Programming the adapteva epiphany 64-core network-on-chip coprocessor[END_REF], [START_REF] Conti | Energy-efficient vision on the pulp platform for ultralow power parallel computing[END_REF]. Taking scaling decisions is a complex issue because variable workload demands have to be taken into account, such that application performance is not negatively impacted. An overview of operating point scaling methods at system level is presented in [START_REF] Zhuravlev | Survey of energy-cognizant scheduling techniques[END_REF]. Among these methods, some employ controllers with a feedback loop because of their abilities to adapt to workload dynamics. Operating points are tuned by looking either at the filling of hardware queues [START_REF] Wu | Formal online methods for voltage/frequency control in multiple clock domain microprocessors[END_REF], [START_REF] Ogras | Design and management of voltage-frequency island partitioned networks-on-chip[END_REF], [START_REF] Garg | Custom feedback control: Enabling truly scalable on-chip power management for MPSoCs[END_REF], [START_REF] Bogdan | Dynamic power management for multidomain system-on-chip platforms: An optimal control approach[END_REF] or software queues, e.g., at task scheduler [START_REF] Juang | Coordinated, distributed, formal energy management of chip multiprocessors[END_REF], at inter-task communication [START_REF] Alimonda | A feedback-based approach to dvfs in data-flow applications[END_REF], [START_REF] Almeida | PI and PID regulation approaches for performanceconstrained adaptive multiprocessor system-on-chip[END_REF]. Existing work proposes low overhead, simple controllers, such as proportional integral derivative (PID) [START_REF] Juang | Coordinated, distributed, formal energy management of chip multiprocessors[END_REF], [START_REF] Carta | A control theoretic approach to energy-efficient pipelined computation in mpsocs[END_REF], [START_REF] Almeida | PI and PID regulation approaches for performanceconstrained adaptive multiprocessor system-on-chip[END_REF] and non-linear [START_REF] Alimonda | A feedback-based approach to dvfs in data-flow applications[END_REF] ones, as well as complex custom controllers [START_REF] Ogras | Design and management of voltage-frequency island partitioned networks-on-chip[END_REF], [START_REF] Garg | Custom feedback control: Enabling truly scalable on-chip power management for MPSoCs[END_REF], [START_REF] Bogdan | Dynamic power management for multidomain system-on-chip platforms: An optimal control approach[END_REF]. Significant energy reductions are reported. The experiments are mostly performed in simulation with the exception of two approaches that target high-performance chips such as Intel's SCC [START_REF] David | Dynamic power management for multicores: Case study using the intel SCC[END_REF] and hexa-core Xeon platforms [START_REF] Ayoub | OS-level power minimization under tight performance constraints in general purpose systems[END_REF]. Nevertheless, most existing methods do not fully address applications that have throughput constraints, which are typical in domains like, computer vision, image and signal processing. Furthermore such applications may have different QoS demands and, depending on the available memory resources of the hardware platform, their buffers may have different sizes. Larger buffer sizes may accommodate larger variations of the workload while allowing the application to still meet the throughput constraint. All these aspects need to be considered when designing a controller that tunes the operating points of hardware blocks.

To this end, the first contribution of this paper is a PIbased controller that addresses data-parallel applications with throughput constraints. These applications execute on a tiled architecture, where each tile is placed in a voltage-frequency island that can be controlled independently. Here we control the speed of each tile, i.e., its clock frequency, assuming that the lowest voltage supply necessary for a given frequency is set by existing methods [START_REF] Altieri | Coupled voltage and frequency control for dvfs management[END_REF]. The controller has two distinct regions, an energy management one where the PI is applied, and a critical one where the tiles will run at their maximum frequency to avoid throughput degradations. The evaluation experiments are performed on a test chip following a tiled multi-VFI architecture [START_REF] Melpignano | Platform 2012, a many-core computing accelerator for embedded socs: performance evaluation of visual analytics applications[END_REF], with a realistic HMAX object recognition application [START_REF] Serre | Object recognition with features inspired by visual cortex[END_REF]. The evaluation metrics are: [START_REF] Panades | A fine-grain variation-aware dynamic Vddhopping AVFS architecture on a 32 nm GALS MPSoC[END_REF] energy reduction (we consider as baseline an execution at maximum frequency), (2) number of frequency switches (often frequency switches bring energy and performance overhead), (3) degree of throughput degradation (here, ideally the controller should always meet the constraint), and (4) the controller overhead. All timing-related numbers, e.g., throughput, number of frequency switches, are realistic and include overheads, e.g, of frequency switch. Energy reductions are estimated off-line using models constructed from physical chip measurements.

The second contribution of this paper is an in-depth experimental analysis of the sensitivity of the PI controller to different configurations. This analysis is meant to determine the best settings and led to the definition of three controller operating intervals, referred to as, the high-amplitude variation, the low-amplitude variation, and the saturation interval. The interval containing the best controller settings depends on the QoS levels and buffer sizes of the application.

The third contribution is a comparison against the performance of an existing non-linear controller with two variants. Experiments indicate that for our use-case, the PI controller attains on average 25% less number of frequency switches, leads to slightly better energy savings than the two nonlinear ones. In addition, the PI controller meets the throughput constraint in cases where the other two approaches fail. All investigated controllers have low overhead.

In the rest of this paper we first present the background information in Section II, followed by the model of our system in Section III and the proposed PI controller. Section IV covers the experimental results, and Section V discusses the related work. Finally Section VI concludes the paper.

II. APPLICATION, ARCHITECTURE

This section covers preliminary information, namely the SoC architecture template and the application model, required to understand this work.

A. Tiled, GALS architecture template

We consider a tiled SoC that follows a general template of Globally Asynchronous Locally Synchronous (GALS) architecture, such as the existing chips [START_REF] Panades | A fine-grain variation-aware dynamic Vddhopping AVFS architecture on a 32 nm GALS MPSoC[END_REF], [START_REF] Melpignano | Platform 2012, a many-core computing accelerator for embedded socs: performance evaluation of visual analytics applications[END_REF]. Figure 1 illustrates this template. Each tile is placed in a separate voltage-frequency island (VFI) and hence its speed and energy consumption can be tuned independently of other tiles. The tiles are connected via an asynchronous network on chip (NoC) that ensures communication. A tile comprises one or more cores, i.e., processor elements (PE), as well as level one memory blocks (L1) and hardware blocks for communication (DMA) and inter-tile synchronization. The tiles may share a level two on-chip memory (L2), accessible over the NoC. The SoC is connected with a host processor, which is responsible with starting and stopping the execution of the tiles and accessing the I/O interfaces. From this perspective, the multi-/many-core can be regarded as a accelerator for the host. The host and the SoC share a high-speed main memory.

B. Data parallel application model

In many domains, e.g., computer vision, image processing, robotics, the application model is data-flow, namely a set of tasks that process a continuous stream of incoming data. These tasks communicate within each other through buffers. Such applications are typically constrained by a throughput demand. This constraint is expressed in, e.g., samples, pixels, entire images, required to be available at each time unit.

Here we address data-flow applications following a common structure with a source task, multiple data parallel worker tasks, and a sink task, as described in Figure 2. The source and the sink tasks are not involved in heavy processing; the source distributes the work (and input data) to the worker tasks and the sink collects the results. We assume that the source task attempts a simple work balancing strategy by splitting the input data in pieces of similar size before sending them to the worker tasks. The worker tasks process input data and store the results in output buffers.

The main concern of the sink node is to respect the throughput constraint, i.e., to make available an output token Fig. 2. Data parallel application model each unit of time. The exact definition of an output token and its size is application dependent. We assume that the sink is not required to collect workers' results in any particular order, meaning it does not block if one of the workers is slower than the others. However, to complete an output token, the sink requires all the tasks that work on that token to have finished. Multiple tokens may be in processing at a given time moment at the worker nodes.

In case that the throughput constraint is not met, i.e., the workers produced insufficient data for the sink, the partially computed output token is discarded. Other scenarios can be implemented here, however we consider this as the most realistic for streaming applications. We denote this shortly as a skipped output. Note that we intentionally avoid the term deadline miss, as we do not address hard real-time applications where a deadline miss leads to severe consequences, but rather applications that have a soft throughput constraint.

C. Implementation

The application is implemented with the Multicore Association Application Programming Interface (MCAPI) [18]. The MCAPI specification defines an API and a semantic for communication and synchronization between processing cores in many-core embedded systems. Our work is not limited to MCAPI, as any other data-flow implementation model that supports processes that communicate through buffers or channels can be used. MCAPI is based on three basic concepts: (1) a node, which is an independent thread of control that executes a program and communicates with other nodes, (2) an endpoint, which is a communication termination point attached to a node; two endpoints can be connected to form a channel, and (3) a domain which consists of a set of MCAPI nodes that are grouped together based on architectural or routing matters. Each node belongs to one single domain. We use the blocking communication in MCAPI. This means that, if a channel is empty/full its consuming/producing node blocks.

We implement each worker task as an MCAPI domain, which will be mapped on a computation tile. Inside a task, a worker may split in threads, each corresponding to a MCAPI node. These threads may execute in parallel on the PEs of the tile; no constraint is imposed on the type of parallel structures used inside a task, e.g., pipeline, data parallel. All the threads of a worker task are scaled together, when the DVFS technique is applied to their underlying tile.

The sink and the source task are mapped on a single MCAPI domain, executing on the host processor. Each of them may have several threads, implemented as nodes. For example, in our case we assign a source and a sink thread to each worker domain such that, even if some of the worker buffers are full/empty, the source/sink may send/collect data from other workers.

III. CONTROL OF THE CLOCK FREQUENCY OF THE TILE

The clock frequency of the different tiles can be controlled in order to reduce energy consumption, however the throughput constraint should be met. Here, four similar tiles are considered, with the throughput equally split over the tiles. An independent, local controller is designed for each tile, following the method below. The system model (subsection III-A), together with the requirements of the closed-loop system, motivate the controller choice (subsection III-B).

A. System modelling

In order to meet the throughput constraint, the sink node should have available from the workers a token of size Y th data units, each ∆ th time units. Here we modify only the tile clock frequency f . Therefore, the objective is to act on f so as to ensure the constraint is fulfilled.

The available data y(k) at time k in the buffer is given by:

y(k) = y(k -1) + Q in (k) -Q out (k) (1)
Q in (k) and Q out (k) are the quantities of data produced by the worker and consumed by the sink, respectively, at time k. Moreover, as we have no direct action on Q out (k), it is considered as a disturbance. Therefore, the z-transform of the system is:

Y (z) Q in (z) = 1 1 -z -1 (2)
which represents an integrator. Moreover, the quantity of data that enters the buffer depends on the producer clock frequency, modeled here by a simple linear equation:

Q in (z) = b • F (z) (3)
with b being an application-dependent parameter. We approximate b with an average value on typical execution traces.

B. Controller design

The system under study is nonlinear, as pointed out in the literature, e.g. [START_REF] Bogdan | Dynamic power management for multidomain system-on-chip platforms: An optimal control approach[END_REF]. However, a linearized model as presented in Section III-A is used in order to design the controller. Indeed, when the system can be modeled with a linear(ized) approximation, simple controllers can be obtained. Such controllers have minimal implementation overhead, unlike controllers relying on complex nonlinear control theory.

Notice that non-linearities, such as saturation and bounded control values exist in the system. Because buffers have limited size, they may become full or empty, leading, in this latter case to a "skipped output". The frequency is also bounded and has discrete values. The presence of saturation can affect the behavior of the closed-loop system, leading to controller performance loss, oscillations and even instabilities. However, the controller is designed such that the system stays far from saturation.

From a control viewpoint, the closed-loop system has to fulfill several requirements:

• Settling time. Because the quantity of data in the buffer should be large enough to guarantee the throughput, we do not need the controller to be highly reactive. This "low" reactive time will have beneficial side effects because the clock frequency will not be subject to fast/strong changes, the opposite leading to extra overhead (in energy and/or time). Hence the settling time, defined as the time required for the available data y to reach the setpoint y SP , does not need to be short;

• Overshoot. Oscillations around y SP are not desired, as they could increase the number of frequency switches;

• Rise time. Here again, the rise time must not be too short in order to avoid rapid (instantaneous) frequency changes as soon as there is some activity at the buffer's input/output;

• Steady state error. We do not have a strong constraint on a reduced steady state error, because, ultimately, the exact level of buffer filling is not important. However, if the steady state error is not brought to zero, the closed-loop system might present inappropriate behavior.

Finally, the controller must ensure the stability of the closed-loop system. Taking into account the system model (2) and the above requirements, the following PI controller is designed:

C(z) = F (z) E(z) = K p + K i z z -1 (4)
where F (z) is the controlled frequency. The error

E(z) is equal to Y SP (z) -Y (z)
, where Y (z) is the available data and Y SP (z) is the setpoint (in z-notations). K p is the proportional gain and K i is the integral gain. The associated recurrence equation is:

f (k) = f (k -1) + (K p + K i )e(k) -K p e(k -1) (5)
Note that the proposed controller being a PI one, during saturation the integral term may increase faster than expected, and the usage of an anti-windup mechanism is mandatory.

K p and K i influence the value of the closed-loop poles, as resulting from Equations ( 2) and ( 4). The closed-loop behavior is fixed via the choice of the closed-loop poles, leading to the computation of the controller parameters. The characteristic equation of the closed loop transfer function is given by:

z 2 + (-2 + K p b + K i b)z + (1 -K p b) = 0 (6)
where the z 1 and z 2 are the poles to be placed:

(z -z 1 )(z -z 2 ) = 0 (7)
By using ( 6) and ( 7), K p and K i can be found:

-z 1 -z 2 = -2 + K p b + K i b (8) z 1 z 2 = 1 -K p b (9)
The closed-loop poles must be in the unit circle to ensure the controlled system stability. Moreover, they must have real values to avoid overshoot. Section IV investigates the performance of the closed-loop system for various pole placements within the (0; 1) interval. In addition, the controller is triggered periodically. Its activation period ∆ ac should be smaller than the time period at which the throughput is enforced, ∆ ac < ∆ th . This is quite similar to the Shannon condition that has to be fulfilled for sampled systems. The PI control will be applied in the so-called "energy management region", as visible in Figure 3. When the buffer filling level becomes lower than the quantity of data that gives the throughput constraint, Y th , the maximum clock frequency is applied to avoid a "skipped output". We consider the case where Y th is a constant value, e.g., decoding applications that need to deliver a constant throughput to a rendering system.

C. Limitations

The present work is limited to the following cases:

(1) Data-parallel application, with simple inter-task datadependencies, e.g., no pipeline support; (2) Local, per-tile, control. Currently, the same controller is implemented for each tile, and no coordination between controllers is present to explicitly address inter-tile variations in workload; [START_REF] Varghese | Programming the adapteva epiphany 64-core network-on-chip coprocessor[END_REF] The system modeling makes several simplifying assumptions. Equation (3) represents a crude approximation for applications behaviour. Furthermore, the work does not straightforwardly apply to cases where neither the output nor the input throughput are constant. Future work will relax these hypotheses by addressing more complex application dependencies, distributed control, and a wider system model.

IV. EXPERIMENTAL RESULTS

To validate our PI controller, we used HMAX, a complex recognition application. This application is a powerful hierarchical framework for object recognition which attempts to mimic the behavior of the human brain [START_REF] Serre | Object recognition with features inspired by visual cortex[END_REF]. Hierarchical recognition typically involves the computation of a set of features at a given level, based on the features computed at the previous level. The input data of the first level is typically a raw image buffer, and the extracted features are the results of multiple filters applied to the input image such as Gabor filters [START_REF] Riesenhuber | Hierarchical models of object recognition in cortex[END_REF].

For the scope of this paper, we consider the first level of the HMAX application, hence the sink node of this HMAX level needs to deliver to a next level a given throughput, expressed in blocks of pixels per second. The application is data parallel.

We investigate the HMAX application for different QoS demand level and buffer size, because these two parameters impact energy management. The QoS demand level indicates the amount of slack available in the application. When the QoS demand is high, the amount of slack available in the application is low, and the other way around. The size of the buffers influences the time window available to utilize the slack. Intuitively, if the buffers are small they will fill up quicker and even if the application has a lot of slack, the workers may block, hence energy would be waisted.

The main metrics considered for evaluation are: (1) energy reductions (here we chose a baseline with no energy management), (2) the number of clock frequency switches, or shortly, number of switches, and (3) the number of skipped outputs. We also present more detailed metrics, e.g., the time in which the workers are blocked on a full buffer, when necessary for the explanation of results. The observed controllers' overhead is low in all cases (under 1%), hence we do not detail it further.

This application executes on a test chip that follows the template described in Figure 1 and embeds four tiles, each with 16 processors [START_REF] Melpignano | Platform 2012, a many-core computing accelerator for embedded socs: performance evaluation of visual analytics applications[END_REF]. We experimented with several input images over tens of seconds of application execution time. Because we utilize a fully-fledged multi-cluster test chip, the performance results, e.g., throughout, number of skipped output, are very realistic. As the test chip does not support dynamic supply voltage scaling, we obtain the energy numbers by utilising the off-line model presented in what follows.

A. Energy model

This work considers only dynamic power because the measured static leakage energy is very small (< 3%) on our test chip. The dynamic energy consumption model is given by the classical equation: E dyn = A • V 2 , where A is a coefficient that represent the circuit activity, and V is the supply voltage. We obtain the parameters of the energy model for the test chip by direct measurements. Static voltage scaling and dynamic frequency scaling are performed to obtained several (V, f ) points. We assume a linear dependency between the clock frequency and the supply voltage, and from the measurement results we interpolate a model of the form:

E dyn = f ∈f levels N f • αf 2 + βf . ( 10
)
where f levels is the set of available frequencies and N f are the number of clock cycles executed at frequency f . Here we consider 6 frequency levels between 200 and 400MHz, however any other configuration can be used.

B. PI poles placement

This section presents the investigation of the controller behaviour function of the poles placement on the real axis, for all cases described in Table I.

As we will see, the controller has three types of poles intervals, where its behaviour, e.g., number of frequency switches, energy reduction, is different. The first is denoted as the high-amplitude variation interval (marked with 1 in figures) and it represents the poles interval where, after largely scaling down the frequency, the controller needs to quickly go We present the results for poles' belonging to the interval [0.6; 0.985]. Outside of this interval the benefits in energy reduction or number of frequency switches diminish.

First, we would like to highlight that no output is skipped, for all QoS levels, regardless of the poles' location.

Second, the results for high QoS demand are presented in Figure 4a and Figure 4b, for the energy reductions and number of frequency switches, respectively. We observe that, when we move from a more reactive control (poles at 0.6) to a less reactive one (poles at 0.985), the energy reduction slightly increases, hence, from this point of view, the controller performs better when the closed-loop system has slower dynamics. This is because, when the controller is less reactive, the slack accumulates, permitting to run longer times at lower frequencies, which is beneficial for energy consumption. Figure 4a also indicates that the buffers never fill up, hence the workers never block, even when the controller is very slow. This is because the QoS demand is maximum.

Furthermore we observe an increase in number of switches, up an inflexion point at 0.95. This is somewhat counterintuitive because one would expect that a less reactive controller would induce fewer frequency switches. However, this is not the case here because the QoS demand is high, hence we do not have a large amount of slack, and thus after scaling down the frequency, the controller needs to quickly go back to higher frequencies where is stays for longer time. In other words we are in the high-amplitude variation interval. This is also indicated by the frequency histogram in Figure 5, which presents the number of time instants when the application runs at given frequencies.

For larger poles (after 0.95), the controlled system becomes slow enough to so that the application accumulates slack and it can run longer times at a lower frequency. This results in a decreasing number of switches and the controller is in the low-amplitude variation interval, using mostly the two highest levels of frequency (350MHz and 400Mhz). This is indicated also by Figure 5: with large poles the clock frequency is less reduced in amplitude (but for longer time periods) and the application spends less time at f max .

The "best" controller corresponds to large poles (at the right end of the low-amplitude interval). However, highly reactive controllers can be chosen from the beginning of the high-amplitude interval, when the desired number of frequency switches must be low, as this zone presents only a 2% lower energy reduction when compared to the low-variation one.

Third, the results for low QoS demand are presented in Figure 6a and Figure 6b, for the energy reductions and number of frequency switches, respectively. Here also the energy reductions slowly increase over the investigated range of poles. We observe a similar behaviour as in the previous case of high QoS demand, with two intervals, namely high-and lowamplitude. However the differences in number of switches in the first interval is not that pronounced because the QoS demand is lower and, hence there is less need to spend a lot of time at higher frequencies. This is why the number of switches has an inflection point earlier, at 0.93. After 0.93 the system enters in the low-amplitude interval where the slack can accumulate and allow large periods at low frequencies. Moreover, for poles larger than 0.97, the energy reductions quickly diminish, because the controlled system is too slow and, as the sink node imposes a low QoS demand, the output buffers fill up. In other words, the controller is in the saturation interval.

In the case of low QoS demands, the "best" controller setting corresponds to closed-loop poles just before the saturation zone. Here, unlike the case of high QoS demand, controllers in the high-variation interval are not interesting because they do not bring a significant reduction in number of switches.

Small buffer sizes

Figures 7 and8 present the results for high QoS and low QoS demand, respectively. In case of small buffer sizes we have similar controller behaviour, i.e., high-amplitude, lowamplitude, saturation, but for different poles' intervals. Furthermore, because the buffers are smaller, the controller saturates much earlier. For example, for low QoS demand, for closedloop poles higher that 0.7, the fact that workers block for more that 1% of the time already causes a decrease in energy reduction, and if the controlled system is not sufficiently reactive, the application will even skip outputs (poles at 0.93). Outputs are skipped in the case the controller is either too reactive or too slow, as visible in Figures 7b and8b.

C. Controllers' comparison

We compare the PI controller proposed in this paper with a state-of-the-art non-linear controller proposed in [START_REF] Alimonda | A feedback-based approach to dvfs in data-flow applications[END_REF], which we denote as the 1-threshold controller. This controller increases or decreases the frequency with one step, if the workers' buffer filling is smaller or larger, respectively, than the setpoint. The controller is triggered at a variable time interval, when the difference in buffer filling is higher than a certain level, to reduce the number of frequency switches. Furthermore, we also compare against an extension that we make to the 1-threshold controller, and that we refer to as the 2-thresholds controller. The 2-threshold controller is quite similar to the 1-threshold one, except that it has a low threshold (to trigger frequency switches when the buffer filling increases) and a high threshold (to trigger frequency switches when the buffer filling decreases). This type of non-linear controller is typically used for processes that require a low number of actuating actions, e.g., temperature regulation, hence it has the potential to reduce the number of switches also in our case. The setpoint is the same for all controllers. The 2-thresholds controller thresholds are at 10% lower/higher that this setpoint.

The results for the case of medium QoS level (0.7 • QoS max ) and different buffer sizes is presented in Figure 9. We can observe that for our use-case application, buffer sizes larger than 5 times the token size do not bring large improvements in number of frequency switches or energy consumption. We observe that the 3 controllers have similar energy reductions, up to 50%, as visible in Figure 9a. The PI controller offers less frequency changes, with an average of 35% and 20% decrease when compared to the 1-threshold controller and 2-thresholds controller, respectively, as indicated in Figure 9b. An important point is that the PI controller skips no output tokens, unlike the non-linear controllers in case of small buffer sizes, as covered by Figure 9c. This means that these controllers are too reactive for the highly constraint case of small buffer sizes.

The results for the case of small buffer sizes, with various QoS levels are presented in Figure 10. Again, we observe that the 3 controllers have similar energy reductions, up to 63% for low QoS levels, as visible in Figure 9a. In term of number of frequency changes, the 2-thresholds controller is close to the 1-threshold one. Furthermore, the PI controller offers less frequency changes than the non-linear ones, with an average reduction of 26% over the entire range of QoS levels, as indicated in Figure 9b. The PI controller skips no output tokens, unlike the non-linear controllers, as presented by Figure 9c.

The results for large buffer sizes are similar; they are not reported due to space limitation.

V. RELATED WORK

The management of operating points has been addressed in the literature for the purpose of reducing energy consumption or mitigate hot-spots. A recent survey of such methods is presented by Zhuravlev et al. [START_REF] Zhuravlev | Survey of energy-cognizant scheduling techniques[END_REF].

Control theoretic strategies have the potential to provide good adaptation solutions for dynamic processes, as proved in many engineering domains. Therefore, they were applied to operating point tuning already in early DVFS approaches for single-core systems [START_REF] Lu | Control-theoretic dynamic frequency and voltage scaling for multimedia workloads[END_REF]. One of the first to study controltheoretic methods for DVFS in multi-processor systems are Juang et al. [START_REF] Juang | Coordinated, distributed, formal energy management of chip multiprocessors[END_REF]. They propose a proportional-integral derivative (PID) controller, and the ideas originate from earlier work by the same authors on multiple clock domain microprocessors [START_REF] Wu | Formal online methods for voltage/frequency control in multiple clock domain microprocessors[END_REF]. The PID controls the clock frequency of each processor by looking at the filling of software tasks queues on each core. Local and distributed methods are compared in simulation, proving a lot of energy saving potential, with a minor performance loss.

Another category of solutions looks at hardware queues in the processor [START_REF] Wu | Formal online methods for voltage/frequency control in multiple clock domain microprocessors[END_REF] or multi-/many-core systems [START_REF] Ogras | Design and management of voltage-frequency island partitioned networks-on-chip[END_REF], [START_REF] Garg | Custom feedback control: Enabling truly scalable on-chip power management for MPSoCs[END_REF]. A custom controller is designed to adapt the frequency depending on the filling of the queues of the network interface of the NoC [START_REF] Ogras | Design and management of voltage-frequency island partitioned networks-on-chip[END_REF], [START_REF] Garg | Custom feedback control: Enabling truly scalable on-chip power management for MPSoCs[END_REF]. This controller is evaluated initially on an FPGA prototype with good results. Furthermore the method is applied on an Intel SSC platform [START_REF] David | Dynamic power management for multicores: Case study using the intel SCC[END_REF] for a data-parallel application following the same model as in our work. As lessons learned, the need for fast voltage switching and for tailored control algorithms is advocated. Recently, the same authors proposed an optimal control approach base on fractalstate equations [START_REF] Bogdan | Dynamic power management for multidomain system-on-chip platforms: An optimal control approach[END_REF]. The controller assumes a platform where operating frequency of PEs and routers can be individually actuated. The experimental workload consists of web-server and data-base applications. The solution seems well tailored for dynamic workload, however it involves on-line linear programming solving, which brings a non-negligible overhead.

The closest approaches to our work are the ones addressing data-flow applications [START_REF] Almeida | PI and PID regulation approaches for performanceconstrained adaptive multiprocessor system-on-chip[END_REF], [START_REF] Alimonda | A feedback-based approach to dvfs in data-flow applications[END_REF]. These bodies of work support a more general application model than our paper because they include pipeline tasks. The SHoP architecture successfully applies a distributed PI(D) controller to adapt the cores' clock frequency and balance multimedia workload over an SoC [START_REF] Almeida | PI and PID regulation approaches for performanceconstrained adaptive multiprocessor system-on-chip[END_REF]. The results indicate that the systems can adapt to perturbations and reach throughput in most cases. In contrast to this work, we propose a controller that explicitly addresses the throughput constraint by having two regions, namely, a critical one and an energy management one. The PI is applied only in the energy management region, when the buffer filling is above the level that would guarantee the fulfilment of the throughput. Below that level the maximum frequency is applied. Furthermore, we extend existing work with an experimental analysis of the controller setting for various QoS levels and buffer sizes.

Alimonda et al. [START_REF] Alimonda | A feedback-based approach to dvfs in data-flow applications[END_REF] propose a threshold-based non-linear controller. The controller is trigger with a variable rate to reduce the number of frequency switches. Energy savings are obtained in simulation for a software FM radio use-case. A comparison of this type of non-linear controller with a PI controller is presented by the same authors [START_REF] Carta | A control theoretic approach to energy-efficient pipelined computation in mpsocs[END_REF], indicating that the PI leads to a higher number of frequency switches. Contrary to these previous findings, we show that, for our usecase, the PI controller results in significantly less frequency switches and slightly less energy consumed than the thresholdbased controller with variable triggering.

In summary, unlike most of the state-of-the-art, this paper addresses applications where no performance loss is desired, i.e., throughput constraint should be firmly respected. We extend state-of-the-art with an investigation the PI configurations that offer the "best" performance, in terms of energy, number of frequency switches, number of skipped outputs, for various demanded QoS levels and buffer sizes levels. Last but not least, we apply and investigate the control on an real GALS test chip, in contrast to most of the existing approaches.

VI. CONCLUSION

This paper addresses the problem of determining the clock frequency of tiles in GALS architectures that execute dataparallel applications with throughput constraints. The solution is a novel PI-based controller with two distinct regions, namely, an energy management one where the feedback control is applied and a critical one where the application runs at maximum frequency. These regions are designed to avoid throughput degradations. We evaluated our controller on a test-chip embedding dynamic frequency scaling and static voltage scaling per tile. All timing-related numbers, i.e., throughput, number of frequency switched, are realistic and include overheads. Energy reductions are estimated off-line using models constructed from physical measurements. We have observed that the best PI controller configuration depends on the application's QoS levels and buffer sizes. Furthermore, we compared the PI with two simple non-linear approaches, i.e., (1) a state-of-the-art controller with one threshold and (2) an improved version of it with two thresholds. All three controllers have low overhead. Experimental results suggest that the PI controller outperforms the state-of-the-art in number of frequency switches (25% less, on average) and energy savings. Furthermore the PI meets the throughput constraint in cases where the other approaches fail.

Fig. 1 .

 1 Fig. 1. Tiled SoC template

Fig. 3 .

 3 Fig. 3. Control regions

Fig. 4 .

 4 Fig.4. Influence of poles placement for large buffer sizes with high QoS back to higher frequencies for longer time. This case occurs for reactive controllers, when QoS demand is high, hence the application does not have a large amount of slack. The second is denoted as the low-amplitude variation interval (marked with 2 in figures) and it represents the poles interval where the frequency is scaled down less but for longer time periods. The third is the saturation interval (marked with 3 in figures), where the workers are blocked because they are either too fast and the output buffers are full, or too slow and the output buffers are empty (skipped outputs). Typically the saturation zone energy is wasted.

Fig. 5 .Fig. 6 .

 56 Fig. 5. Histogram of clock frequencies, large buffer sizes, high QoS 1. Large buffer sizes

Fig. 7 .

 7 Fig. 7. Influence of poles placement for small buffer sizes with high QoS

Fig. 8 .

 8 Fig. 8. Influence of poles placement for small buffer sizes with low QoS

Fig. 9 .Fig. 10 .

 910 Fig. 9. Comparison of 3 controllers for medium QoS level (0.7 • QoSmax), various buffer sizes

TABLE I .

 I INVESTIGATED COMBINATIONS OF DEMANDED QOS AND

		BUFFER SIZES
		High QoS demand	Low Qos demand
		(QoSmax)	(0.5 • QoSmax)
	Large buffer size	Low amount of slack	High amount of slack
		Large slack utilization window	Large slack utilization window
	Small buffer size	Low amount of slack	High amount of slack
		Small slack utilization window	Small slack utilization window

ACKNOWLEDGMENT

This work was partially supported by the Artemis JU, the Catrene JU, and the French Ministere de l'Economie, du Redressement productif et du Numrique, under Grant Agreement n • 332913 (project COPCAMS) and Grant Agreement n • CA112 (project HARP).


Lourdes Diaz Olvera

Didier Plat
email: didier.plat@entpe.fr

Pascal Pochet
email: pascal.pochet@entpe.fr

Lourdes Diaz Olvera
email: lourdes.diaz-olvera@entpe.fr

Assessment of mobility inequalities and income data collection. Methodological issues and a case study (Douala, Cameroon)

Keywords: Household travel survey, income data collection, daily mobility, transport expenditure, mobility inequality, sub-Saharan Africa

come     Assessment of mobility inequalities and income data collection. Methodological issues and a case study (Douala, Cameroon)

INTRODUCTION

In metropolitan areas that are experiencing marked spatial growth, as is the case in sub-Saharan Africa, access to the activities and resources afforded by the city is far from universal. This is primarily because of socio-geographical disparities in the distribution of urban services and jobs [START_REF] Myers | Disposable Cities: Garbage, Governance and Sustainable Development in Urban Africa[END_REF][START_REF] Rakodi | The urban challenge in Africa[END_REF]. However, the situation is further worsened by major inequalities in the use of motorised transport modes, not only cars but also public transport which is too expensive for poor city-dwellers to use on a regular basis [START_REF] Bryceson | Livelihoods, daily mobility and poverty in Sub-Saharan Africa[END_REF][START_REF] Diaz Olvera | The puzzle of mobility and access to the city in Sub-Saharan Africa[END_REF][START_REF] Lucas | Making the connections between transport disadvantage and the social exclusion of low income populations in the Tshwane Region of South Africa[END_REF][START_REF] Salon | Mobility, poverty, and gender: Travel "choices" of slum residents in Nairobi, Kenya[END_REF][START_REF] Sietchiping | Transport and mobility in sub-Saharan African cities: An overview of practices, lessons and options for improvements[END_REF].

Differences between individuals' travel behaviours obviously exist, in the same way that there are differences between their state of health and access to healthcare and, in the case of the young, their possibility of going to school. When such differences between individuals result in disadvantages with regard to daily mobility, they are perceived as inequalities if they are due to situations that are partially or completely unchosen (income, gender, age, physical capacities, accessibility of residential location, etc.). In sub-Saharan Africa, transport policies take little account of the issues of social and geographical equity, i.e. the goal of fostering a more equal access to mobility, and, more broadly, to urban resources.

Investments in urban transport are usually focused on the construction and maintenance of roads and benefit primarily the minority of citizens with private cars [START_REF] Vasconcellos | Urban Transport, Environment and Equity. The case for developing countries[END_REF]. The Bus Rapid Transit systems which have recently been built, or which are currently planned, in many large African cities (Addis Abeba, Dakar, Dar es Salaam, Lagos, etc.) could indicate a change of policy direction, but it is still too early to assess if they will be affordable and located where they can serve low income populations. Both these conditions must be satisfied if the mobility of the poor is to improve. [START_REF] Teunissen | Mapping Equality in Access: The Case of Bogotá's Sustainable Transportation Initiatives[END_REF] have shown, for example, in the case of Bogotá, that while the Transmilenio serves the zones with the greatest concentrations of poor people, its cost means they are unable to make much use of it. Such decisions on the part of the public authorities are explained by a variety of factors such as the role of international organisations and donors or the desire to have "modern" transport systems which use up-todate technology. But even if the public authorities wished to consider the impacts of transport policy with regard to equity, they would in most cases be unable to do so because of an absence of adequate statistical data. The knowledge of the scale and nature of intra-urban inequalities requires reliable statistics disaggregated by income group [START_REF] Mitlin | City inequality[END_REF]. Such income statistics must then be compared with travel behaviours. But as the investigation of travel issues is frequently concerned with engineering considerations, data collection is still very much focused on the travel of economically active groups [START_REF] Behrens | Collection of passenger travel data in Sub-Saharan African cities: Towards improving survey instruments and procedures[END_REF].

It is never straightforward to collect income data in household surveys, in particular because of refusals to respond and the fact that the amounts involved are, deliberately or not, inaccurately reported. Researchers have investigated this issue in countries of the North (see, in particular [START_REF] Davern | The effect of income question design in health surveys on family income, poverty and eligibility estimates[END_REF][START_REF] Hansen | Does how you measure income make a difference to measuring poverty? Evidence from the UK[END_REF][START_REF] Micklewright | How reliable are income data collected with a single question[END_REF][START_REF] Moore | Income measurement error in surveys: A review[END_REF][START_REF] Scott | Generating relevant household level data: Multi-topic household surveys[END_REF]. In the case of travel surveys in countries like the United States or Australia, [START_REF] Stopher | Collecting, Managing, and Assessing Data Using Sample Surveys[END_REF] recommends asking respondents to indicate a relatively wide income band rather than state the exact amount in order to reduce nonresponse rates. The issue of collecting income data in surveys has, however, been considerably less studied in developing countries, even though the estimation of income poses particularly great problems there [START_REF] Pettersen | Survey design and sample design in household budget surveys[END_REF][START_REF] Deaton | The analysis of household surveys: A microeconometric approach to development policy[END_REF][START_REF] Deaton | Consumption[END_REF]. In theory, a more satisfactory approach would be to evaluate the standard of living on the basis of household expenditure [START_REF] Deaton | Consumption[END_REF], but the complexity and cost of a protocol of this type means that it cannot be implemented in a household travel survey [START_REF] Diaz Olvera | Household transport expenditure in Sub-Saharan African cities: Measurement and analysis[END_REF]. The direct collection of individuals' incomes in these surveys is therefore indispensable. However, it raises three sets of difficulties, particularly in Africa.

First, several factors make it difficult to estimate the income derived from work. In this context where the amount of paid employment is falling and the number of informal microactivities is on the rise, many workers depend on precarious jobs and occasional work, for which they are paid irregular amounts at irregular times (De Vreyer and Roubaud, 2013). For the numerous self-employees, like petty traders or low-skilled craftpersons, it is difficult to estimate the net profit drawn from their activity as no accounts are kept. Similarly, in the case of young women, for example in apprenticeships, it is not at all easy to distinguish labour from domestic or nonremunerated activities. In addition, it is common for individuals to have a number of activities, and this applies not only to individuals in paid employment who do so in order to diversify their sources of income and to save, but also to individuals working in the informal sector, who do so in an attempt to compensate for the irregular nature of their principal activities [START_REF] Bocquier | Employment vulnerability and earnings in urban West Africa[END_REF][START_REF] Ersado | Income diversification in Zimbabwe: Welfare Implications from Urban and Rural Areas[END_REF][START_REF] Iyenda | Street enterprises, urban livelihoods and poverty in Kinshasa[END_REF].

Second, income cannot be restricted to the sums that are earned from professional activities. It also includes grants and benefits, rents, pensions and, above all, gifts from one individual to another. Particularly in the case of the latter, it is difficult to estimate the sums involved because of the irregular nature of the transfers. But even if chains of solidarity are tending to weaken [START_REF] Abdullah | Gender and Adjustment in Nigeria's Manufacturing Sector[END_REF]Leimdorfer and Marie, 2003;[START_REF] Séraphin | Vivre à Douala : L'imaginaire et l'action dans une ville africaine en crise[END_REF], gifts from outside the household continue to contribute significantly to the total income of individuals and households, particularly among the poor [START_REF] Lourenço-Lindell | Walking the Tight Rope: Informal Livelihoods and Social Networks in a West African City[END_REF].

Last, the economic behaviour of the population and the role of the household also add to the difficulty of estimating standards of living on the basis of income. Individuals are often unaware of the personal resources of the other members of their household, and not all income is pooled [START_REF] Glick | Schooling of girls and boys in a West African country: the effects of parental education, income, and household structure[END_REF][START_REF] Hoddinott | Does female income share influence household expenditures? Evidence from Côte d'Ivoire[END_REF][START_REF] Posel | Intra-family transfers and income-pooling[END_REF][START_REF] Yapi-Diahou | Baraques et pouvoirs dans l'agglomération abidjanaise[END_REF]. Among other things, the implication of this for transport is that access to motorised modes is more strongly conditioned by an individual's personal monetary resources than by those of his or her household [START_REF] Diaz Olvera | Household transport expenditure in Sub-Saharan African cities: Measurement and analysis[END_REF][START_REF] Venter | Gender, residential location, and household travel: Empirical findings from low-income urban settlements in Durban, South Africa[END_REF].

The aim of this paper is thus to evaluate in what way income data collection affects the accuracy of data and therefore the measurement of mobility inequalities. We have done this by referring to a household travel survey conducted in Douala (Cameroon) in 2003 in which respondents' income data was collected in a disaggregate and precise manner. The estimated values of mobility inequalities obtained from this survey have been compared with what was observed from less sophisticated data collection. This data was not the outcome of specific fieldwork conducted at the same time as the travel survey but was obtained from ex post simulations which provide less accurate income data, that are comparable with those obtained from surveys that collect income data in a much simpler way. The case study provides a variety of information about mobility inequalities in Douala. However, our aim is not to analyse their determinants or to identify policies that might reduce them, but rather to evaluate how their measurement is affected by a number of methodological decisions.

After a short description of the local context of Douala, Section 2 describes the income data collection procedure used for the travel survey and presents the simulation method. Section 3 uses the results of the simulations to show how the quality of income data affects the measurement of inequalities in daily travel and transport expenditure for individuals and households. Section 4 concludes on the benefits of detailed individualised income data collection for the measurement of inequalities in daily mobility and in transport expenditure.

DATA AND METHOD

The PMU survey ("Pauvreté et Mobilité Urbaine", Poverty and Urban Mobility) carried out in 2003 aimed to analyse the links between poverty, daily mobility and access to urban services in Douala1 . Urban areas were stratified according to the availability of urban services, how long ago they became urbanised, distance from the centre and major roads, and the standard of living of the residents. Thirty survey zones were then selected within the stratified areas and the sample of households was selected randomly within the survey zones. 600 households and 1885 individuals of over 10 years of age were surveyed by face-to-face interviews in their home [START_REF] Sitrass | Poverty and Urban Mobility in Douala[END_REF].

The study zone

Douala is Cameroon's most populous city, with nearly 2 million inhabitants in 2003. It is also a port and the main gateway for imports and exports. Douala is the country's economic capital and provides the location for more than half the country's economic activity and industrial production. Economic activity is nevertheless dominated by the informal sector which employed 62% of the workforce in 2005. As a result of the low level of wages, 14% of the population have at least two professional activities (De Vreyer and Roubaud, 2013).

The city has developed in a site that is subject to severe geographical constraints. Some informal districts have sprung up in swampy zones or on natural drainage courses or slopes. The Wouri River which crosses the city also poses a major constraint for transport, since the only bridge between the two banks creates a notorious bottleneck (Figure 1). * The nearest public transport stop is less than 15 minutes away on foot ** The nearest public transport stop is 15 minutes or more away on foot As in other cities of sub-Saharan Africa, in Douala walking is still the population's principal means of transport. Access to private vehicles is very limited and motorised trips are mainly made on public transport [START_REF] Diaz Olvera | The puzzle of mobility and access to the city in Sub-Saharan Africa[END_REF] which is provided by six modes: shared taxi, motorbike taxi, minibus, bus, light truck, undeclared cab. Most public transport trips are made by shared taxis, but the modal share of motorbike taxis is rapidly increasing, as they are less expensive over short distances and can provide a door-to-door service. The ease with which residents can access a public transport mode from their home varies according to the availability of roads and public transport in the district in which they live and access and egress segments made on foot may be long. Walking access and egress times allow us to identify which of the survey zones are accessible -when the place of residence is on average less than 15 minutes from the loading point -, and which zones are remote -when it is 15 minutes or more away 2 .

2 This dichotomous spatial indicator is crude, due to a lack of exhaustive data about the districts' accessibility and facilities. It does not allow us to measure a gradient of increasing difficulty in access and only takes account of one dimension of the accessibility problem, namely access to public transport.

Capturing professional activities and income in the PMU Survey

The PMU survey collected data at two levels. First, at the level of the household, the reference individual provided information on the composition of the household, the dwelling, and access to basic services and infrastructure. Second, each individual of over 10 years of age was interviewed personally, with the focus placed on his or her socio-economic characteristics, access to private vehicles, expenditure on transport and trips made on the day before the interview.

With regard to socio-economic characteristics, several sets of questions provided precise information about each individual's professional activities and income 3 . First of all, a set of questions allowed us to list each professional activity exercised by the respondent. Each individual was asked if he/she was currently engaged in a professional activity and if so:

1. the nature of the principal activity, its frequency (over the last 12 months and the last 30 days) and for how long the individual had been doing it (Figure 2). This information allowed us to calculate annual incomes; 2. the description of any remunerated secondary activities (Figure 3). A secondary activity is defined as a supplementary professional activity practiced by an individual currently in employment (i.e. in the past 30 days)4 .

No. Question 29. Have you been gainfully employed (in cash or in kind) in the past 30 days? 30. Is this a permanent job? 31. Are you a salaried employee? 33. Description of principal activity 39. For how long have you been engaged in this activity? (number of years) 40. How many months did you work out of the past 12 months? 41. How many days did you work out of the past 30 days?

Fig. 2. Identification of principal activity in the PMU survey

3 By interviewing each respondent it is possible to overcome biases which result from the use of a single informant for an entire household [START_REF] Fisher | Who should be interviewed in surveys of household income?[END_REF]. Insofar as the reference individual is not necessarily correctly informed about the situation of each household member, it would appear to be questionable to rely only on his or her statements.

No. Question 36. Do you have other activities that generate income in cash or in kind? 37. How many? 38. What are these activities?

Fig. 3. Identification of secondary professional activities in the PMU survey

With regard to income, our aim was to assess as accurately as possible the individual's total monetary resources, by mentioning a variety of potential sources, which may or may not be linked to professional activities (Figure 4). Respondents were left free to estimate their earnings from each source according to the most appropriate periodicity. There are two advantages to this more detailed data collection procedure:

-As an individual can have several sources of income, listing them during the interview helps to reduce omissions;

-Whatever the periodicity reported by the respondent, each type of income can be extrapolated on a monthly or annual basis in order to estimate a total sum.

In this paper, we have harmonised the separate incomes to express them in monthly terms, then consolidated them for each individual; the sum of individual incomes has been used to estimate the household's total income.

The survey protocol makes it very clear that the income data should relate to money earned outside the household in order to avoid double counting. In particular this prevents the counting of monetary transfers between members of the household (pocket money, paying for meals taken outside the household). Particular attention was paid to the collection of income data during the training of field staff in order to make them aware about variable periodicities, the difference between turnover and profit and the need to avoid double counting if several members of the household take part in the same economic activity.

No.

The evaluation of income data in the PMU survey

It is possible to compare the sources of income that were collected in the PMU survey with those collected during a survey that dates from 2002, namely the CAVIE survey (INS, 2003). This survey collected information on the living conditions of 7500 households: infrastructure and basic services, services in the dwelling, durable goods. Household composition and information on all members of the household were also included in the survey.

Two major methodological differences with the PMU should be noted:

a single informant was questioned in each household in order to provide not only general information about the household, but also specific information on each individual; the single informant was asked whether each member of the household had worked in the last twelve months (and if so in which sector), about his/her main sources of income and the sums involved, broken down into two categories, professional and other. These two amounts were expressed as a bracket.

As a result of these methodological differences, the distribution of individuals (of over 10 years of age) according to the principle source of income differs considerably between the two surveys (see the second and third columns of Table 1). While the CAVIE survey reports that one in two individuals had no income, the PMU survey gave a ratio of one in four. The differences were moderate when we compared the proportions of individuals whose work was their principal source of income, but the PMU survey reported a higher proportion of individuals receiving pensions or rents and, in particular, receiving mainly gifts. This is because the information relating to the individual was collected directly from him/her and also because these sources of income were identified specifically in the questionnaire (Questions 55 to 58, Figure 4). The sums involved were often small, particularly in the case of gifts5 . Nevertheless, these gifts from outside the household were frequently the only source of income for schoolchildren and the economically inactive.

Measuring mobility inequalities, simulating degraded data collection

Mobility practices were measured using two categories of indicators:

-Physical indicators, which were measured at the individual level, are the number of trips (total and motorised) and the travel time budget (total and motorised).

-Monetary indicators were estimated for individuals and for households. In both cases, the monthly expenditures on urban transport, for all modes and solely for public transport modes, were computed6 . The proportion of household income spent on urban transport was also calculated.

Inequalities have been evaluated using concentration curves and concentration indices group's share of the indicator will be exactly equal to its relative size in the population. In this case, the cumulative percentages of both the indicator and the population will be exactly equal whatever population segment is considered. Graphically, the closer the plot is to the line of equal distribution (the first diagonal), the more equally the indicator is distributed among the population and the lower its concentration index. Mathematically, the latter is equal to 1 minus twice the surface area between the plot and the abscissa.

In order to produce a concentration curve or index it is therefore necessary to be able to class the population of individuals or households according to their standard of living. In the case of individual mobility indicators, the individual's income provides a better idea of his/her ability to access motorised modes than the income of the household [START_REF] Diaz Olvera | Household transport expenditure in Sub-Saharan African cities: Measurement and analysis[END_REF] and therefore allows us to estimate the individual's standard of living. In the case of household indicators, ranking households according to their total income means that a given income provides the same standard of living to an individual living alone, a couple, or a family with several children. In order to make the conversion from income to standard of living, economists use an equivalence scale that expresses the differing needs of different individuals (adults and children in particular) and the economies of scale that result from household size (e.g. a couple

does not necessarily need twice the amount of space in their home as a single person).

Determining an equivalence scale is however a complex problem that has raised much controversy [START_REF] Lechêne | Une revue de la littérature sur les échelles d'équivalence[END_REF]. In the absence of a consensus, we adopt what Deaton and Zaidi have termed the "arbitrary method" (2002:51) which involves, in the case of poor countries, considering a low cost for a child and a low economy of scale coefficient, in our case respectively 0.25 and 0.10. The number of individuals in the household is thus replaced by a number of consumption units which is equal to:

(A + α . K) (1-β) where A is the number of adults, K the number of children, α = 0.25 and β = 0.10. The standard of living of the household is then estimated on the basis of the total household income divided by the number of consumption units. Finally households are ranked according to these estimated standards of living.

This methodological basis allows us to calculate mobility inequality indicators, when an estimate of individual incomes is available. An additional stage is necessary in order to assess how the precision of income data collection affects the measured mobility inequalities. This consists of comparing the observed value of the indicator with that which would have been obtained if the distribution of individuals according to their principal source of income had been the same in the PMU and CAVIE surveys. We are, of course, unable to observe this situation.

However, we can use the available data to simulate it.

The simulation method can be summarised as follows. The distribution of individuals on the basis of their principal source of income as reported in the CAVIE survey, which identified more individuals without incomes, was applied to the sample from the PMU survey, which meant that randomly selected respondents had their incomes reset to zero. The proportion of such individuals with their incomes reset to zero depends on the nature of their principal source of income (see last column in Table 1). It was 11.4% when the principal source of income was labour, i.e. approximately one in nine individuals in this category, 55.9% when it consisted of allowances, rents or other sources and 86.9% when gifts were the principal source of income.

In each simulation the distribution of individuals according to their principal source of income was therefore equivalent to that obtained from the CAVIE survey 7 .

To correct for the random nature of resetting the income of one individual to zero rather than another, we carried out a large number of simulations in order to estimate the stability of the 7 This simulation strategy allows us to simulate "realistic" populations. In the simulations, each individual's mobility is accurately estimated, but the individuals (and therefore the households) are incorrectly classified because the data on their income is incorrect. The error in the estimation of inequality is therefore due to the combination of two sources of error: an erroneous classification of individuals and an erroneous estimation of mobility for a given income level. This simulation method was preferred to one which involves directly duplicating the individuals that are already present in each principal income source category until a distribution similar to that in the CAVIE survey is obtained. This is because an alternative strategy of this type would accurately estimate mobility for each income level thereby eliminating a potential source of error in the inequality calculation.

mobility inequality measures. For each inequality measurement, the value observed in the PMU survey can be compared to the median of the simulated values, as well as to the amplitude of the distribution of the simulated values 8 . We thus determined, for each inequality measurement, the number of simulations that is required in order for the estimates of the median value and the amplitude to become stable. This number varied slightly depending on the inequality measurement in question, but never exceeded 500. The results presented below are therefore based on a unique set of 500 simulations.

IMPACTS OF THE INCOME DATA COLLECTION METHOD ON THE MEASUREMENT OF MOBILITY INEQUALITIES

We shall begin by considering the physical indicators of mobility, then move on to the monetary indicators. For a given mobility indicator, if the observed value of the inequality measurement and the median simulated value are close together and the dispersion of the simulated values is small, the income data collection method has little impact on the mobility indicator. If there is a large disparity between the two values, particularly if the observed value is outside the range of the simulated values, it means that our perception of the inequalities is biased when the income data is collected in a simplified manner.

Inequalities according to physical indicators

The total number of trips and the daily travel time budget are the indicators that are the most equally distributed according to the income of individuals. As shown by Figure 5, they are also those for which the impact of a precise measure of income is the most limited: the median of the simulated values is indistinguishable from the observed value and the range of the simulated values is very narrow. Differences for these mobility indicators according to income tend to diminish because citizens with low income or no income at all compensate for their lower access to motorised modes by intensive walking. This explains why the values of the corresponding concentration indices are close to zero 9 . 8 The central tendency parameter of the distribution of the inequality indicators calculated from the simulated incomes is the median rather than the mean value, due to the risk of extreme values appearing in the case of some simulations. For the same reason, when the amplitude of the distribution of the inequality indicators was estimated, the 2.5% of extreme values at the bottom and the top of the distribution were excluded. 9 As the concentration plots for the number of trips and the travel time budget for all modes are almost flat and indistinguishable from the first diagonal, they are not shown here.

Fig. 5. Observed and simulated concentration indices for number of trips and travel time budget (all modes and motorised modes)

The benefits of collecting accurate income data increase when the travel indicators are limited to motorised modes. As can be seen in Figures 6 and7, the plots for the simulated income distributions are above the plot for the observed distribution 10 and the largest differences between curves are concentrated in the bottom half of the distribution. This means that collecting aggregated data reduces inequalities with regard to motorised travel. With regard to the concentration indices (not shown here), the observed value is at best indistinguishable from the upper bound of the range of simulated values and at worst above this bound. The simulated concentration indices are about 90% of those obtained for the observed data. It is important to note that this underestimate does not affect the entire population in the same way and is essentially due to an inaccurate evaluation of the situation regarding the poorest half the population, as shown by the concentration curves.

10 In order to improve the comprehensibility of the figures and facilitate their interpretation, only six curves have been plotted for each: that obtained directly from the PMU survey and five simulations randomly chosen from amongst the five hundred. If we take account of the residential location of the individual's household, distortions in our representation of spatial inequalities become apparent. Once again, the effects are rather negligible in the case of the indicators for all modes (Figure 8). However, use of motorised modes, which is more unequally distributed within remote zones, is more inaccurately measured when income data collection is simplified. For these districts, the observed inequality is greater than the simulated values while it is near the median of the simulated values for the accessible zones. Moreover, the range of simulated values is very large in the case of the remote zones and leads to a partial superimposition of the distributions of simulated values for the two types of zones. Consequently, in between 1% (number of motorised trips) and 2% (motorised travel time budget) of simulations, inequality is greater in the accessible zones than in the remote zones, while the observed concentration index is greater in the remote zones than in the accessible zones by almost half. Excessively aggregated collection of income data may therefore lead to an underestimation of inequalities in each type of zone, and sometimes to a false impression of the relative situation in the two types of zone.

Inequalities according to monetary indicators

The benefit of the precise estimation of incomes is even clearer when we consider the concentration of individuals' travel expenditure (Figures 9 and 10). Once again, almost all the simulated plots are above the observed plot throughout the distribution. The differences are particularly marked for the bottom half of the distribution. The result is a significant underestimate of the inequalities as the concentration indices for the simulated values only attain 85% of those for the source data.

Remote area R

Households spend on average 17% of their budget on daily travel, but this proportion varies according to their standard of living. As can be seen in Figure 13, transport accounts for a lower share of expenditure as households become more well-to-do. According to the observed values, daily travel absorbs almost a quarter of the resources of the poorest households (first quartile), a fifth of those in the second quartile and about a seventh of those in the most well-to-do half of the population (quartiles 3 and 4). The simulated distributions also show a tendency for the budgetary coefficient to fall as household resources increase. But the estimated coefficients are in this case systematically greater than those that have been observed, the bias once again varying greatly according to the wealth of the household. The situation of the more well-to-do is accurately represented, but there is an overestimation of 4% for the two intermediate quintiles and of approximately 50% of the total income in the case of the poorest households. In the case of this last group, the coefficients obtained from the simulations are clearly totally unrealistic.

Such high values would mean that households would then have only a very small proportion of their income left to live on (food, housing, education, clothes, etc.).

Q1 corresponds to the poorest households and Q4 to the wealthiest. By taking account of residential location we can observe similar trends: there is a deterioration in the quality of the estimation from the wealthy to the poor which leads to unrealistic estimations for the first quartile whatever the type of zone (Figure 14). There is also a relative inversion of the position of the two types of area for the poorest half of the population. Once again, incomplete or inaccurate income data collection leads to an erroneous estimate of the budgetary coefficient of transport, in particular for the poorest households.

Q1 corresponds to the poorest households and Q4 to the wealthiest.

Fig. 14. Proportion of household income devoted to daily mobility, according to income quartile and type of residential zone

CONCLUSION

The income data collection method used in the PMU survey removes the majority of the difficulties that were mentioned in the introduction:

the detailed listing of professional activities of whatever nature and scale makes it easier subsequently to collect more reliable data on income from work;

the explicit mentioning of a variety of sources of income (gifts, pensions, rents, etc.) considerably increases the reported sums; allowing the respondent to select the periodicity with which he or she reports income brings the situation described in the survey closer to real practices; conducting a specific interview for each individual avoids the need to rely on a single informant who may not be very well aware of the situations of individual household members.

However, the methodology that we have chosen does not allow us to perceive the scale of the pooling of individual income within the household, but the opening of the "black box" of the household (Alderman et al., 1995:15) remains a theoretical and empirical problem.

Of course, these options are expensive in terms of both respondent burden and survey cost. But our analyses have shown that more precise data collection improves the estimation of mobility inequalities. Indeed, the data collection method has a direct impact on the ranking of individuals and households in terms of standard of living. In turn, the ranking of individuals and households has impacts on the measurement of inequalities as regards mobility and transport expenditure.

Our analysis shows that the effect of more accurate income data is minor in the case of aggregated indicators (e.g. overall number of trips, travel time budget for all modes, or household level indicators) and for the most affluent groups (individuals and households). On the contrary, the most significant impacts concern disaggregated indicators (e.g. number of motorised trips, motorised travel time budget or individual level indicators). But when there is an effect, it is systematically in the same direction. Simplified data collection tends to minimise the scale of inequalities and the error is greater in remote zones than in accessible zones. This differentiated effect is absolutely clear, in spite of the limitations of our spatial indicator. It is also to some degree independent of the effect of the household's standard of living. Finally, the errors in the ranking of households lead to estimate, in the case of the poorest households, very high and therefore improbable proportions of household income spent on transport. Shortcomings in the methodological apparatus blur our perception of the social and spatial situation of underprivileged groups and distort our assessment of mobility inequalities.

Ultimately, they impede investigation of the links between daily travel, poverty and social exclusion. It seems essential to improve the way income data is collected in surveys in order to obtain a more accurate picture of the mobility inequalities linked to households' and individuals' standards of living and their residential location. This need applies beyond the case of Douala. Making similar comparisons to those presented here in other urban contexts, in other African countries, or even in other developing or developed regions, would allow us to evaluate the extent to which the lessons we have learned from Douala can be generalised. Nevertheless, similar effects to those we have revealed in Douala are likely to pertain to other African cities. The reason for this is that large African cities share a considerable number of features: the jobs market is dominated by the informal economy, there are large inequalities with regard to income and widespread poverty, rapid spatial expansion, a lack of basic facilities, low private vehicle ownership rates and a public transport system which is informal, inefficient and unsubsidised. In situations of this type it is particularly important to be able to evaluate accurately the redistributive nature of urban public transport policies. A thorough knowledge of daily travel practices is one requirement for this and accurate collection of individual income data is another which is just as essential.

Fig. 1 .

 1 Fig. 1. The conurbation of Douala and the survey zones in the PMU household travel survey(2003)

  Fig. 4. The collection of individual income data in the PMU survey

(

  [START_REF] O'donnell | Analyzing Health Equity Using Household Survey Data: A Guide to Techniques and their Implementation[END_REF]. The concentration curve provides a graphic representation of the proportionality of the distribution of an indicator (number of daily trips, travel time budget, transport expenditure) in relation to the population (individuals or households), which is ranked according to increasing income. It plots the cumulative percentage of a mobility indicator (yaxis) against the cumulative percentage of the population, ranked from the poorest to the richest (x-axis). If the indicator is distributed among the population in a perfectly equal manner, any

Fig. 6 .

 6 Fig. 6. Concentration curves for number of motorised trips: observed distribution and five simulated distributions of individual income

Fig. 8 .

 8 Fig. 8. Observed and simulated concentration indices for number of trips and travel time budget (all modes and motorised modes), according to type of residential zone

Fig. 9 .

 9 Fig. 9. Concentration curves for public transport expenditure: observed distribution and five simulated distributions of individual income

Fig. 11 .

 11 Fig. 11. Observed and simulated concentration indices for individual and household transport expenditure

Fig. 13 .

 13 Fig. 13. Proportion of household income devoted to daily mobility, according to income quartile

  Type of monetary resources (CFA francs)

		Do you	Periodicity	Amount
		receive...	1. Daily
		1. Yes	2. Weekly
		2. No	3. Monthly
			4. Quarterly
			5. Half-yearly
			6. Annually
			7. Other ..........
	51.	Wages / salary / profit from principal activity
	52.	Wages / salary / profit from secondary activity (activities)
	53.	Wages / salary / profit from other professional activities
	54. Total labour income (51+52+53)
	55. Annuities
	56.	Grants, gifts, alimony, allowances, etc. (from persons outside household)
	57. Family allowances, pensions, scholarships
	58.

Table 1

 1 Distribution of individuals according to their principal source of income and probabilities used to simulate income distributions for the PMU survey sample

		PMU survey	CAVIE survey	Relative
		(%)	(%)	disparity
		(a)	(b)	(a-b)/a
	Individuals with an income	74.5	48.5
	Professional activities	49.4	43.8	0.114
	Allowances, rent or other	4.5	2.0	0.559
	Gifts	20.6	2.7	0.869
	Individuals with no income	25.5	51.5
	Total	100.0	100.0

The PMU survey was carried out by a team composed of French and Cameroonian researchers, including the authors of this paper, who were responsible for the project's general methodology, in particular the survey questionnaire.

The level of multiple activities measured by the PMU survey was 12%, which is close to the value obtained by De Vreyer and Roubaud (2013).

These gifts accounted for less than 10% of all the income reported in PMU survey. They accounted, of course, for an even smaller proportion according to the CAVIE survey, but it is impossible to calculate the exact percentage as income data was only recorded in the form of a bracket.

To collect information on public transport expenditure, individuals were asked how many times they used each of the six modes of public transport and the corresponding amount spent during the past seven days. In motorised households, the running costs of vehicles were collected on a monthly basis (fuel) or annually (maintenance, repairs, insurance, licensing).