Frédéric Ridouard
email: frederic.ridouard@enseeiht.fr

Jean-Luc Scharbarg
email: jean-luc.scharbarg@enseeiht.fr

Christian Fraboul
email: christian.fraboul@enseeiht.fr

Stochastic network calculus for end-to-end delays distribution evaluation on an avionics switched Ethernet

AFDX (Avionics Full Duplex Switched Ethernet, used for modern aircraft such as Airbus A380 represents a major upgrade in both bandwidth and capability for aircraft data networks. Its reliance on Ethernet technology helps to lower some of the implementation costs, though the requirement for guaranteed service does present challenges to system designers.

Thus, the problem is to prove that no frame will be lost by the network (no switch queue will overflow) and to evaluate the end-to-end transfer delay through the network.

Several approaches have been proposed for this evaluation. Deterministic network calculus gives a guaranteed upper bound on end-to-end delays, while simulation produces more accurate results on a given set of scenarios. In this paper, we propose a stochastic network calculus approach in order to evaluate the distribution of end-to-end delays. We evaluate the pessimism of the results on some typical AFDX flows, as described by Virtual Links.

Introduction

The evolution of avionics embedded systems and the amplification of the integrated functions number in the current aircraft imply a huge increase in the exchanged data quantity and thus in the number of connections between functions. Consequently, the growth of the number of multi point communication, such as the development of embedded networks, constitutes one of the major stakes of new generation architectures.

The solution adopted by Airbus for the new A 380 generation consists in the utilization of a recognized standard which allows a re-use of development tools as well as of existing communication components while achieving better performance. It consists of the Switched Ethernet technology which benefits from a long industrial use [START_REF]IEEE 802.1D, Local and Metropolitan Area Network: Media Access Control Level Bridging[END_REF], that allows to have confidence in the reliability of the material and on the facility of its maintenance. Hence aeronautical systems can integrate of a much more powerful technology than the traditional avionics bus (Switched Ethernet / 100 Mbps). AFDX (Avionics Full Duplex Switched Ethernet) [START_REF]Aircraft Data Network, Part 1: Systems Concepts and Overview[END_REF][START_REF]Aircraft Data Network, Part 2: Ethernet Physical and Data Link Layer Specification[END_REF][START_REF]Aircraft Data Network, Part 7: Deterministic Networks[END_REF] is a static switched Ethernet network (802.1D tables are statically set up and no spanning tree mechanism is implemented) for determinism purpose. The full duplex switched Ethernet technology guarantees that there are no collisions on the physical links, compared with a vintage Ethernet solution [START_REF] Jasperneite | Deterministic Real-Time Communication with Switched Ethernet[END_REF]. So, it eliminates the inherent indeterminism of vintage Ethernet and the collision frame loss. But, it shifts in fact the problem to the switch level where various flows will enter in competition for the use of the resources of the switches. This can lead to temporary congestion on an output port of a switch, if at a given time, too much traffic moves towards this port. This can increase significantly end-to-end delays of frames and can even lead to frame losses by overflow of queues.

Flows on an AFDX network are statically identified in order to obtain a predictable deterministic behavior of the application on the network architecture. The analysis of end-to-end delays of frames is necessary in order to characterize the behavior of the application. This analysis has to evaluate, on the one hand an upper bound on the end to end delay of a given flow, on the other hand the distribution of this end-to-end delay. The first one is mandatory for certification reasons, while the second one can help greatly to evaluate the pessimism of the upper bound and is valuable when prototyping the whole system. In this paper, we consider that there is no frame loss (queues are large enough) and we study end-to-end delays distribution of frames. Preliminary results have been presented in [START_REF] Charara | Focusing simulation for end-to-end delays analysis on a switched Ethernet[END_REF], considering a simulation approach. In this paper, we consider a stochastic network calculus approach.

Section 2 specifies the end-to-end delays analysis problem in the context of this paper. Section 3 presents the stochastic network calculus approach. Section 4 gives some results and evaluate their pessimism. Section 5 summarizes the paper and gives some guidelines for future works.

Scope of the study

In this section, we first give a brief overview of the AFDX network. Then, we formulate the problem of endto-end delay analysis and the way it is addressed in the remaining of the paper.

The AFDX network

An example of an AFDX network architecture is depicted Figure 1. It corresponds to a test configuration provided by Airbus for an industrial research study [START_REF] Charara | Methods for bounding end-to-end delays on an AFDX network[END_REF]. It is composed of several interconnected switches. There are no buffers on input ports and one FIFO buffer for each output port. The inputs and outputs of the networks are called End Systems (the little circles on Figure 1). Each End System is connected to exactly one switch port and each switch port is connected to at most one End System. Links between switches are all full duplex. In Figure 1, values on input and output end systems indicate numbers of application traffic flows. For instance, there are 113 different application traffic flows that are directly transmitted from an end system to switch S1. The end-to-end traffic characterization is done by the definition of Virtual Links. As defined by ARINC-664, Virtual Link (VL) is a concept of virtual communication channels; it has the advantage of statically defining the flows which enter the network [START_REF]Aircraft Data Network, Part 7: Deterministic Networks[END_REF].

End Systems exchange Ethernet frames through VL. Switching a frame from a transmitting to a receiving End System is based on a VL (deterministic routing). The Virtual Link defines a logical unidirectional connection from one source End System to one or more destination End Systems. It is a path with multicast characteristic. The routing of each VL is statically defined by the designer. He arbitrarily chooses one path between the source and end destination fo the VL. One possible criterion is the load balancing between links. Only one End System within the Avionics network can be the source of one Virtual Link, (i.e., Mono Transmitter assumption).

Traffic on each Virtual Link is sporadic. Most of the time, physical links of an AFDX network are lightly loaded. As an example, on the configuration of Figure 1, most of the links are loaded at less than 15 % and no link is loaded at more than 21 % (see [START_REF] Charara | Methods for bounding end-to-end delays on an AFDX network[END_REF] for details). However, a congestion can occur at any time at any output port in case of a transient burst of traffic. This lead to variable end-to-end delays for frames of a given VL. Bursts of traffic occur when frames of different VLs reach the same output port at the same time. This event is closely related to the emission of the frames of the different VLs, i.e. the phasing between VLs.

Scope of the end-to-end delay analysis

Frames exchanged between End Systems have to respect temporal constraints. So, the end-to-end delay of each path of each VL has to be studied. It includes the following characteristics :

• upper bound for the end-to-end delay, which corresponds to the longest aggregate waiting service time for the frame in queues. Studies have been done in order to evaluate this upper bound. Deterministic Network Calculus approach [START_REF] Cruz | A calculus for network delay, part I[END_REF][START_REF] Cruz | A calculus for network delay, part II[END_REF] gives the latency upper bound of any elementary network entity.

Then, guaranteed upper bounds on end-to-end delays can be derived [START_REF] Frances | Using network calculus to optimize the AFDX network[END_REF][START_REF] Boudec | Application of network calculus to guaranteed service networks[END_REF]. Most of the time, those bounds cannot be reached as they are based on pessimistic assumptions. An open question is to determine how pessimistic those bounds are. The model checking approach [START_REF] Alur | Theory of Timed Automata[END_REF][START_REF] Larsen | UPPAAL in a Nutshell[END_REF] determines an exact upper bound for the end-to-end delay and the corresponding scenario [START_REF] Charara | Methods for bounding end-to-end delays on an AFDX network[END_REF][START_REF] Ermont | Worst-case analysis of a mixed can/switched ethernet architecture[END_REF], but it cannot be applied to a realistic network configuration, due to combinatorial explosion. Nevertheless, this approach can help greatly to better understand the behavior of the network.

• The distribution of the end-to-end delay between its lower bound and its upper bound. Simulation is a promising approach to obtain this distribution, provided it covers a representative subset of all possible scenarios. Preliminary results have been presented in [START_REF] Charara | Focusing simulation for end-to-end delays analysis on a switched Ethernet[END_REF]. They have been obtained by focussing the simulation on the relevant part of the network configuration, using a taxonomy of VLs. However, simulation can't cope with too large network configurations, due to their huge number of possible scenarios.

In this paper, we propose a stochastic network calculus approach in order to obtain a distribution of end-to-end delays. Such an approach could deal with arbitrarily large network configurations. The next section presents the stochastic network calculus approach.

Stochastic network calculus analysis

First, we explain why stochastic network calculus theory can be applied in the AFDX context. Then we show how we apply stochastic network calculus results to our context.

Applicability of the analysis

As mentioned earlier, the aim is to obtain the distribution of end-to-end delay for a given path of a VL. The AFDX networks considered in the present study have a single FIFO buffer for each switch output port. That means that flows (VLs) all have the same priority. Consequently, each switch output port can be considered as servicing an aggregate traffic (all the VLs crossing this port) with a constant rate c which is the capacity of the output link (e.g. 100 Mbps). Moreover, the individual flows are shaped separately at network access, by the assumption of the minimum delay between the emission of two consecutive frames, i.e. BAG (Bandwidth Allocation Gap). It corresponds to a network considering EF PHB (Expedited Forwarding Per-Hop Behavior) service of DiffServ (Differentiated Services) architecture [START_REF] Davie | An expedited forwarding PHB (per-hop behavior)[END_REF]. The nodes (i.e. the switch output ports) are said PSRG (Packet Scale Rate Guarantee) nodes [START_REF] Bennett | Delay jitter bounds and packet scale rate guarantee for expedited forwarding[END_REF] and the EF traffic at a node is served with a rate independently of any other traffic transiting the same node. The stochastic network calculus approach presented in [START_REF] Vojnović | Stochastic analysis of some expedited forwarding networks[END_REF] applies to such network configurations.

More formally, a node is PSRG (c,e) for a flow means this flow is guaranteed a rate c, with a latency (error term) e. Therefore if we denote d n , the departure of the n th packet of the EF aggregate flow, in order of arrivals, d n satisfies

d n ≤ f n + e
where f n is calculated recursively as f 0 = 0 and

f n = max {a n , min{d n-1 , f n-1 }} + l n c , n ≥ 1
where the n th packet arrives at time a n with l n bits.

The error term e is the extra waiting time due to non EF traffic. In our context, there is only EF traffic crossing each switch output port. Consequently, we have e = 0.

The end-to-end delay of a given path of a VL is the sum of the delays in each switch crossed by the path. The delay in a switch is composed of the switching delay (filtering and forwarding operations), the waiting time in the output buffer and the transmission time on the output link. The switching delay is a constant that depends on the switch technology (16 µs for switches used by Airbus). The transmission time is a function of the link rate (typically 100 Mbps). The waiting time of a frame depends on the load of the output port (backlog) at the arrival time of the frame. Therefore, the end-to-end delay is not constant due to the waiting times in the switch output ports it crosses.

The works presented by Vojnović and Le Boudec in [START_REF] Vojnović | Stochastic analysis of some expedited forwarding networks[END_REF][START_REF] Vojnović | Bounds for independent regulated inputs multiplexed in a service curve network element[END_REF] about networks with EF PHB service can be used to calculate the distribution of this waiting time for each switch. It is based on the probability of bound buffer overflow in the switch output port. Such a problem was previously addressed in [START_REF] Chang | On the performance of multiplexing independent regulated inputs[END_REF][START_REF] Kesidis | Worst-case performance of a buffer with independent shaped arrival processes[END_REF]. Results presented in [START_REF] Vojnović | Stochastic analysis of some expedited forwarding networks[END_REF][START_REF] Vojnović | Bounds for independent regulated inputs multiplexed in a service curve network element[END_REF] have proposed the tightest upper bounds.

Vojnović and Le Boudec make the four assumptions presented in appendix A. The assumption (A1) imposes to define a service curve for nodes. But a property of PSRG is that a PSRG (c, 0) implies the service curve β(t) = ct. Consequently, the property (A1) is respected.

As VLs are independent at network access, assumption (A2) is respected. Concerning assumption (A3), in the AFDX context, each VL is regulated by a leaky-bucket (α i (t) = ρ i t + σ i ) defined in the following way. σ i is the maximum length of a frame of the VL, denoted S max . ρ i is the VL maximum flow, Smax BAG , where BAG is the minimum delay between the emission of two consecutive frames of the VL by its source end system. Therefore assumption (A4) is valid with ξ i = ρ i .

Vojnović and Le Boudec define the concept of EF traffic inputs homogeneously regulated (see appendix A). In our context, traffic inputs are homogeneously regulated when all VLs have the same S max and BAG and they are heterogeneously regulated otherwise. Results in [START_REF] Vojnović | Stochastic analysis of some expedited forwarding networks[END_REF] have been proved for homogeneous and heterogeneous cases, while better results are presented in [START_REF] Vojnović | Bounds for independent regulated inputs multiplexed in a service curve network element[END_REF] for homogeneous cases.

As all the assumptions made by Vojnović and Le Boudec are respected, their results can be applied in our context.

Application of the analysis

In [START_REF] Vojnović | Stochastic analysis of some expedited forwarding networks[END_REF], the tightest backlog bound that holds for homogeneous and heterogeneous regulation of traffic inputs is established. This bound gives the distribution of the backlog and is presented in the theorem 1 of appendix B.

There exists in [START_REF] Vojnović | Bounds for independent regulated inputs multiplexed in a service curve network element[END_REF] a tighter bound given by Theorem 2 of appendix B. But this bound holds only for the homogeneous case.

These definitions of probability (Theorem 1 and 2) can be seen as a fraction of time the backlog is above the level b. In order to determine the waiting delay in the output buffer, we need to know the backlog in the buffer at the arrival time of a frame f . It is called the complementary distribution of the backlog. Informally, it is the probability that the size of all frames in the output buffer, including f exceeds the level b. This probability is denoted P A and named the Palm probability [START_REF] Baccelli | Elements of queueing theory[END_REF]. Vojnović and Le Boudec proved corollary 1 of appendix B.

Let d(0) denoted the delay through a node of a frame arriving in the node at time 0. The Theorem 3 of appendix B presents the distribution of delay. P(d(0) > u) is the probability that d(0) exceeds u.

In order to determine the distribution of the end-to-end delay of a given VL, we first compute P(d(0) > u) with u = 0.5, 1.5, 2.5, . . .

until P(d(0) > u) = 0
We have

P(d(0) > 0) = 1 and P(d(0) > u) ≥ P(d(0) > u + 1)
Finally, we consider

P(d(0) = u) = P(d(0) > u -0.5) -P(d(0) > u + 0.

First results

The stochastic analysis presented in the previous section has been applied to AFDX network configurations. First results are presented in this section. They all concern paths of VL, similar to the vx path of Figure 2. The first ones comes from (r-1) End Systems e 2 to e r . Each of those End Systems emits a given number of VLs (n i VLs for End System e i ), among which some have e q as destination End System (m i VLs for End System e i ).

The other inputs of sy, as well as paths of VLs that do not cross sy have no influence on path e1syeq of VL vx and can be ignored in the analysis.

It has been shown in [START_REF] Charara | Focusing simulation for end-to-end delays analysis on a switched Ethernet[END_REF] that the vx path of Figure 2 corresponds to about 12 % of the paths of a typical industrial AFDX configuration.

Results presented in this paper concern the configurations of table 1.

S1 corresponds to a typical VL path of the industrial AFDX configuration of Figure 1. The load of the single switch output port crossed by the VL under study is about 2 %. Configurations S2 to S6 concerns VLs paths similar to S1 with a higher load on the switch output port (between 12 % and 51 %). Since all those configurations contain homogeneous flows, formulas of theorems 1 (V1 approach) and 2 (V2 approach) can be applied. V2 does not apply to the configuration of Figure 1, since flows are not homogeneous.

Figures 3 and4 present the distributions obtained with the V1 and V2 stochastic network calculus approaches presented in section 3.

With the V1 approach, delays for configuration S1 are mostly distributed between 60 and 87 µs. The distribution of delays moves to higher values when the load on the With the V2 approach, we obtain similar distributions with smaller intervals (between 35 and 48 µs for S1, between 50 and 109 µs for S6). As expected, the V1 approach is more pessimistic than the V2 one. Remember however that the V2 approach can't apply when flows are heterogeneous.

In order to evaluate the relevance of those results we have to state, on the one hand the pessimism of the obtained distribution, on the other hand how far it is from the deterministic upper bound.

We have studied the first point by comparing stochastic network calculus approach results with simulation results obtained with the approach presented in [START_REF] Charara | Focusing simulation for end-to-end delays analysis on a switched Ethernet[END_REF]. Figure 5 presents simulation results on S1, S4 and S6.

Figure 5. Simulation

It appears that the simulation approach gives significantly smaller end-to-end delays than the stochastic net- More precisely, it gives for each network configuration the upper bound that the end-to-end delay will exceed with a probability of 0.0001, considering the simulation approach results and the stochastic network calculus results. We can see that the difference between the simulation and the V1 stochastic approaches increases with the load on the switch output port (40 vs 87 for a load of 2 %, 80 vs 311 for a load of 51 %). It means that the pessimism of the V1 stochastic network calculus approach increases with the load of the switch output port. Conversely, the difference between the simulation and the V2 stochastic approaches evolves in a quite linear way.

In second step, we compared the distribution obtained with the stochastic network calculus approaches with the upper bound obtained by a deterministic network calculus approach. Table 2 gives the upper bound computed for each network configuration (see [START_REF] Charara | Methods for bounding end-to-end delays on an AFDX network[END_REF] for details). It shows that the difference between the deterministic upper bound and the stochastic upper bounds that can be exceeded with a probability of 0.0001 increases with the load on the switch output port (106 or 311 vs 2086 for a load of 51 %). It clearly shows that the deterministic approach is much more pessimistic than the stochastic one.

Finally, Figure 6 summarizes results of all the approaches for S1 scenario.

Conclusion

In this paper, we detail the scope of end-to-end delays analysis on an industrial switched Ethernet network. Two important characteristics are the upper bound of end-toend delays and their distribution. The first one is mandatory for certification reasons. The second one can help greatly to evaluate the pessimism of the upper bound and is valuable when prototyping the whole system.

Then we present a stochastic network calculus approach that gives an evaluation of the distribution of endto-end delays of a given flow. The obtained distribution is pessimistic, compared with the real behavior of the network estimated by a simulation approach, but much less pessimistic that the upper bound obtained by a deterministic network calculus approach.

The evaluation presented in this paper only concerns mono-switch flows, which represent about 12 % of a typical industrial network configuration [START_REF] Charara | Focusing simulation for end-to-end delays analysis on a switched Ethernet[END_REF]. However, generalization of this approach to multi-switches flows is underway.

Figure 1 .

 1 Figure 1. AFDX network architecture

Figure 2 .

 2 Figure 2. Monoswitch path

Figure 3 .Figure 4 .

 34 Figure 3. Stochastic network calculus V1

Figure 6 .

 6 Figure 6. Upper bound vs distribution

Table 1 . studied configurations

 1

	5)

Table 2 . Upper bound vs distribution work

 2 calculus approaches. Table2gives a rough comparison of the three approaches results.

		Simu	St. NC	Det. NC
		P = 0.9999 P = 0.9999 Det. NC
			V2	V1
	S 1	40	48	87	103
	S 2	48	58	167	500
	S 3	54	66	213	896
	S 4	61	76	250	1293
	S 5	69	89	282	1689
	S 6	80 106	311	2086

A function, f , is said super-additive if f (s + t) ≥ f (s) + f (t) for all s, t ≥ 0.

A. Definitions and assumptions of Vojnović

• let A(t) = I i=1 A i (t) be the input aggregate.

• α(t) = I i=1 α i (t) denotes the aggregate arrival curve.

• ρ = I i=1 ρ i denotes the upper bound on the aggregate sustainable rate.

• τ is the intersection between the aggregate arrival curve α and the service curve β :

be the backlog at time t of a node.

• let Q(t) be an upper bound of the backlog and

Definition 1

The EF traffic inputs are homogeneously regulated, if they are regulated by the same function :

, for all i ∈ {1, . . . , I}. Otherwise, the EF traffic inputs are heterogeneously regulated.

Vojnović and Le Boudec make the following assumptions :

(A1) Nodes offer to the EF aggregate traffic, a service curve β, means that for all t (t ≥ 0), there exists s, (s ≤ t) such that

where A(t) denote (resp. A * (t)) the input (resp. the output) EF aggregate data from the node on the interval [0,t].

(A2)

The EF traffic inputs are mutually independent at network ingress points.

Let A i (1 ≤ i ≤ I) be the independent EF input traffic.

(A3) Every EF input is regulated at the network ingress point. Consequently, for all i, (1 ≤ i ≤ I), there exists a wide-sense increasing function α i (called arrival curve) such that :

where A 0 i (t) represents the data observed on [0,t] of the input traffic A i at the network ingress.

for any K ∈ N, and any 0 =

Theorem 2 Homogeneous case : Assuming (A1)-(A4) and if ρ < c, for any t, the upper bound of the probability (denoted P) that the backlog is above a given level b is

for any K ∈ N, and any 0 = s 0 ≤ s 1 ≤ . . . ≤ s K = τ . where,

Corollary 1 Let a node that offers a service curve β(t) = ct and A denote the input aggregate with stationary increments and intensity ρ (ρ < c). Then, if a packet arrives in the node at time 0, it holds,

Theorem 3 For a PSRG(c, 0) node and for u ≥ 0, it is established that, if a node arrives in node at time 0, P(d(0) > u) ≤ P A (Q(0) > cu)


Frédéric Ridouard
email: frederic.ridouard@enseeiht.fr

Jean-Luc Scharbarg
email: jean-luc.scharbarg@enseeiht.fr

Christian Fraboul
email: christian.fraboul@enseeiht.fr

STOCHASTIC NETWORK CALCULUS FOR END-TO-END DELAY EVALUATION OF AVIONICS MULTI-HOP VIRTUAL LINKS

Keywords: Network calculus, end-to-end-delay, AFDX, stochastic

The VL (Virtual Link) concept used by AFDX network of modern aircraft such as A380 represents a big assumption for input flows characteristics. But mapping of many VL on a multi switch Ethernet architecture lead to potential congestion on a port of a (given) switch. Thus, there is strong need to prove that no frame will be lost by the network (no switch queue will overflow) and to evaluate the end-to-end transfer delay through the network. Several approaches have been proposed for this evaluation. Deterministic network calculus gives a guaranteed upper bound on end-to-end delays, while simulation produces more accurate results on a given set of scenarios. Stochastic network Calculus has been successfully used to calculate end-to-end delays distribution of mono switch flows. In this paper, we show how it can be extended to multi switches flows.

INTRODUCTION

The evolution of avionics embedded systems and the amplification of the integrated functions number in the current aircraft imply a huge increase in the exchanged data quantity and thus in the number of connections between functions. Consequently, the growth of the number of multi point communication, such as the development of embedded networks, constitutes one of the major stakes of new generation architectures.

The solution adopted by Airbus for the new A 380 generation consists in the utilization of a recognized standard which allows a re-use of development tools as well as of existing communication components while achieving better performance. It consists of the Switched Ethernet technology which benefits from a long industrial use IEEE 802.1D, Local and Metropolitan Area Network: Media Access Control Level Bridging. (1998), that allows to have confidence in the reliability of the material and on the facility of its maintenance. Hence aeronautical systems can integrate of a much more powerful technology than the traditional avionics bus (Switched Ethernet / 100 Mbps). Concepts andOverview. (2002), ARINC 664, Aircraft Data Network, Part 2: Ethernet Physical andData Link Layer Specification. (2002) and ARINC 664, Aircraft Data Network, Part 7: Deterministic Networks. (2003) is a static switched Ethernet network (802.1D tables are statically set up and no spanning tree mechanism is implemented) for determinism purpose. The full duplex switched Ethernet technology guarantees that there are no collisions on the physical links, compared with a vintage Ethernet solution Jasperneite et al. (2002). So, it eliminates the inherent indeterminism of vintage Ethernet and the collision frame loss. But, it shifts in fact the problem to the switch level where various flows will enter in competition for the use of the resources of the switches. This can lead to temporary congestion on an output port of a switch, if at a given time, too much traffic moves towards this port. This can increase significantly end-to-end delays of frames and can even lead to frame losses by overflow of queues.

AFDX (Avionics Full Duplex Switched Ethernet) AR-INC 664, Aircraft Data Network, Part 1: Systems

Flows on an AFDX network are statically identified in order to obtain a predictable deterministic behavior of the application on the network architecture. The analysis of end-to-end delays of frames is necessary in order to characterize the behavior of the application. This analysis has to evaluate, on the one hand an upper bound on the end to end delay of a given flow and on the other hand the distribution of this end-toend delay. The first one is mandatory for certification reasons, while the second one can help greatly to evaluate the pessimism of the upper bound and is valuable when prototyping the whole system. In this paper, we consider that there is no frame loss (queues are large enough) and we study end-to-end delays distribution of frames. Preliminary results have been presented in Charara et al. (2006a), considering a simulation approach. In this paper, we consider a stochastic network calculus approach.

Section 2 specifies the end-to-end delays analysis problem in the context of this paper. Section 3 presents the stochastic network calculus approach for a mono switch and its application to multi switches. Section 4 gives some results and evaluate their pessimism. Section 5 summarizes the paper and gives some guidelines for future works.

SCOPE OF THE STUDY

In this Section, we first give a brief overview of the AFDX network. Then, we formulate the problem of end-to-end delay analysis and the way it is addressed in the remaining of the paper.

The AFDX network

An example of an AFDX network architecture is depicted in Figure 1. It corresponds to a test configuration provided by Airbus for an industrial research study [START_REF] Charara | Methods for bounding end-to-end delays on an AFDX network[END_REF]. It is composed of several interconnected switches. There are no buffers on input ports and one FIFO buffer for each output port. The inputs and outputs of the networks are called End Systems (the little circles on Figure 1). Each End System is connected to exactly one switch port and each switch port is connected to at most one End System. Links between switches are all full duplex. In Figure 1, values on input and output end systems indicate numbers of application traffic flows. For instance, there are 113 different application traffic flows that are directly transmitted from an end system to switch S1. Traffic on each Virtual Link is sporadic. Most of the time, physical links of an AFDX network are lightly loaded. As an example, on the configuration of Figure 1, most of the links are loaded at less than 15 % and no link is loaded at more than 21 % (see [START_REF] Charara | Methods for bounding end-to-end delays on an AFDX network[END_REF] for details). However, a congestion can occur at any time at any output port in case of a transient burst of traffic. This lead to variable end-to-end delays for frames of a given VL. Bursts of traffic occur when frames of different VLs reach the same output port at the same time. This event is closely related to the emission of the frames of the different VLs, i.e. the phasing between VLs.

Scope of the end-to-end delay analysis

Frames exchanged between End Systems have to respect temporal constraints. So, the end-to-end delay of each path of each VL has to be studied. It includes the following characteristics :

• The upper bound for the end-to-end delay, which corresponds to the longest aggregate waiting service time for the frame in queues. Studies have been done in order to evaluate this upper bound. Deterministic Network Calculus approach Cruz (1991a) and Cruz (1991b) gives the latency upper bound of any elementary network entity. Then, guaranteed upper bounds on end-toend delays can be derived Frances et al. (2006) and Le Boudec (1998). Most of the time, those bounds cannot be reached as they are based on pessimistic assumptions. An open question is to determine how pessimistic those bounds are. The model checking approach [START_REF] Alur | Theory of Timed Automata[END_REF] and Larsen et al. (1997) determines an exact upper bound for the end-to-end delay and the corresponding scenario [START_REF] Charara | Methods for bounding end-to-end delays on an AFDX network[END_REF] and [START_REF] Ermont | Worst-case analysis of a mixed can/switched ethernet architecture[END_REF], but it cannot be applied to a realistic network configuration, due to combinatorial explosion. Nevertheless, this approach can help greatly to better understand the behavior of the network. • The distribution of the end-to-end delay between its lower bound and its upper bound. Simulation is a promising approach to obtain this distribution, provided it covers a representative subset of all possible scenarios. Preliminary results have been presented in Charara et al. (2006a). They have been obtained by focussing the simulation on the relevant part of the network configuration, using a taxonomy of VLs. However, simulation can't cope with too large network configurations, due to their huge number of possible scenarios.

In this paper, we propose a stochastic network calculus approach in order to obtain a distribution of end-toend delays. Such an approach could deal with arbitrarily large network configurations. The next section presents the stochastic network calculus approach.

STOCHASTIC NETWORK CALCULUS ANALYSIS

The objective of these works is to obtain the distribution of end-to-end delay for a given path of a VL. The stochastic network calculus, applied to mono switch flows, has already presented in Ridouard et al. (2007). But we detail again this approach in section 3.1. Then, we describe the method to obtain the distribution of end-to-end delay for a given path of a VL crossing several switches.

End-to-end delay for a given mono hop path of a VL

In this section, we are only interested about mono switch. We, first, explain why stochastic network calculus theory can be applied in the AFDX context.

Then we show how we apply stochastic network calculus results to our context.

3.1.1. Applicability of the analysis In the present study, the AFDX networks considered, have only a single FIFO buffer for each switch output port. Consequently, all the flows (VLs) have the same priority and each switch output port can be considered as servicing an aggregate traffic (all the VLs crossing this port) with a constant rate c which is the capacity of the output link (e.g. 100M bps). Moreover, the individual are shaped separately at network access, by the assumption of the minimum delay between the emission of two consecutive frames, i.e. BAG (Bandwidth Allocation Gap). It corresponds to a network considering EF PHB (Expedited Forwarding Per-Hop Behavior) service of DiffServ (Differentiated Services) architecture [START_REF] Davie | An expedited forwarding PHB (per-hop behavior)[END_REF]. The nodes (i.e. the switch output ports) are said PSRG (Packet Scale Rate Guarantee) nodes [START_REF] Bennett | Delay jitter bounds and packet scale rate guarantee for expedited forwarding[END_REF] and the EF traffic at a node is served with a rate independently of any other traffic transiting the same node. The stochastic network calculus approach presented in Vojnović and Le Boudec ( 2002) applies to such network configurations.

More formally, a node is PSRG (c, e) for a flow means this flow is guaranteed a rate c, with a latency (error term) e. Therefore if we denote d n , the departure of the n th packet of the EF aggregate flow, in order of arrivals, d n satisfies

d n ≤ f n + e
where f n is calculated recursively as f 0 = 0 and

f n = max {a n , min{d n-1 , f n-1 }} + l n c , n ≥ 1
where the n th packet arrives at time a n with l n bits.

The error term e is the extra waiting time due to non EF traffic. In our context, there is only EF traffic crossing each switch output port. Consequently, we have e = 0.

The end-to-end delay of a given path of a VL is the sum of the delays in each switch crossed by the path.

The delay in a switch is composed of the switching delay (filtering and forwarding operations), the waiting time in the output buffer and the transmission time on the output link. The switching delay is a constant that depends on the switch technology (16 µs for switches used by Airbus). The transmission time is a function of the link rate (typically 100 Mbps). The waiting time of a frame depends on the load of the output port (backlog) at the arrival time of the frame. Therefore, the end-to-end delay is not constant due to the waiting times in the switch output ports it crosses. , where BAG is the minimum delay between the emission of two consecutive frames of the VL by its source end system. Therefore assumption (A4) is valid with ξ i = ρ i .

Vojnović and Le Boudec define the concept of EF traffic inputs homogeneously regulated (see appendix A). In our context, traffic inputs are homogeneously regulated when all VLs have the same S max and BAG and they are heterogeneously regulated otherwise.

In the following, we consider only homogeneous traffic inputs.

As all the assumptions made by Vojnović and Le Boudec are respected, their results can be applied in our context.

Application of the analysis In Vojnović and

Le Boudec (2003) the tightest backlog bound (given by Theorem 1 of appendix B) for homogeneous regulation of traffic inputs is established.

These definitions of probability (Theorem 1) can be seen as a fraction of time the backlog is above the level b. In order to determine the waiting delay in the output buffer, we need to know the backlog in the buffer at the arrival time of a frame f . It is called the complementary distribution of the backlog. Informally, it is the probability that the size of all frames in the output buffer, including f exceeds the level b. This probability is denoted P A and named the Palm probability [START_REF] Baccelli | Elements of queueing theory[END_REF]. Vojnović and Le Boudec proved Corollary 1 of Appendix B.

Let d(0) denoted the delay through a node of a frame arriving in the node at time 0. The Theorem 2 of appendix B presents the distribution of delay. P(d(0) > u) is the probability that d(0) exceeds u.

End-to-end delay for a given multi hop path of a VL

In this section, we present the method used to obtain the distribution of the end-to-end delay of packet. The packet crosses a network and follows the path of a VL from source to destination.

Unfortunately, the stochastic Network Calculus analysis is valid only for VL crossing a mono switch Ridouard et al. (2007). To apply the stochastic network calculus for a given multi hop path of a VL, a solution is to calculate the delay crossing each switch and finally to sum up the different delays. But a known property for network calculus is the Pay Bursts Only Once Le Boudec and Thiran (2001). This property shows that the results obtained are not tighter. Then we cannot extend the first results Ridouard et al. (2007) obtained for mono switch, to multi hop path without analysing the propagation of the end-to-end delay. But there exist results for deterministic Network Calculus for VL with multi hop path :

Considering the following assumptions :

• Independent input flows,

• Inputs flows are regulated by leaky buckets,

• Each switch is e FIFO service curve

In Le Boudec and Thiran ( 2001), the authors demonstrate that if theses assumptions are respected, for a given multi hop path of a VL, the switches crossed can be concatenated to an only switch with an arbitrary service curve. And the problem can be transform to an only VL and an only switch. Let V L 1 be a VL crossing n (n > 0) switches, e S -S 1 . . . S n -e q and illustrated by the Figure 2. e S represents the end system source of V L 1 and e q its end system destination. S i (i ∈ {1, . . . , n) denotes the output port of the i th switch crossed by V L 1 .

Fig. 2. V L 1 , the VL crossing two switches

In Le Boudec and Thiran (2001), it has been proved that the arrival curves of input flows of the same output port can be aggregated. Consequently, without loss of generality, we consider only the case of two flows coming in each output buffer, f 1, the flow of V L 1 and the flow aggregated of others flows. To determine the delay through a node of a frame, we must determine the service curve to the flow of the frame.

In Le Boudec and Thiran (2001), the authors prove that if β i (t) = R t + T be the service curve of a node S i and if each node

S i (1 ≤ i ≤ n) serves two flows f 1 and f 2 (the flow f i (i = 1, 2) has an arrival curve α i (t) = ρ i t + σ i . If ρ 1 + ρ 2 < R), then for S i , the flow f 1 has a service curve equals to β f 1 i (t) = (R - ρ 2 )t + T + σ2
R . Moreover, at the output, the flow f 1 has the arrival curve α * 1 (t) = ρ 1 t + σ 1 + ρ 1 (T + σ2 R ). Then, for the flow f 1, we can determine the arrival curve and the service curve for each node S i (1 ≤ i ≤ n) and all the nodes of the path can be reduce to an Fig. 3. The node created for V L 1 only node, as illustrated by the Figure 3. For the flow f 1, the node created, has the following service curve :

β f 1 = β f 1 1 ⊗ β f 1 2 ⊗ • • • ⊗ β f 1 n
Where β f 1 i is the service curve of the flow f 1 for the node S i And ⊗, the min-plus convolution given by :

(f ⊗ g)(t) = inf 0≤s≤t {f (s) + g(t -s)}.
But for the flow f 1, the node created has a service curve β f 1 , with the form β f 1 (t) = Rt + T where R is the rate to serve f 1 and T , the waiting time before serve. To apply the works presented in Section 3.1, the service curve must be super-additive (i.e. β(t + s) ≥ β(t) + β(s)) and then T ≤ 0. But T is a waiting time (T > 0) and the service curve β f 1 is not superadditive. We can resolve this problem : we use the following service curve: β f 1 (t) = Rt to compute the end-to-end delay. T is summed up to the final worst case end-to-end delays, since T is a waiting timeis summed up to the final worst case end-to-end delays.

We are assumed that flows are homogeneous. But since for each VL we just consider one switch and one flow (the given VL), we can erase this assumption for the following of our works.

Using the works developed for the deterministic network calculus Le Boudec and Thiran (2001), we can apply the stochastic network calculus (presented in Section 3.1) since the problem is transformed to a mono hop path.

RESULTS ON TWO HOP VL

In this section, the stochastic Network Calculus analysis presented in the previous section, is applied to AFDX network configurations. The network configuration is composed of three switches, five paths of VL and six end systems. It is depicted by the Figure 4. Table 2. Upper bounds of end-to-end delay c = 100b/µs (see section 3.1.1). Each path supports the same number of VL and all VLs of the network configuration have the same end system destination, e q . In our context, traffic inputs are homogeneously regulated (see section 3.1.1) then, all VLs have the same length S max (= 4000 bits) and same BAG (= 4000µs).

In this section, we study VL crossing two switches. Therefore, we do not calculate the distribution of endto-end delay of VL with the path e 5 -S 3 -e q . Moreover, VLs are homogeneous and each path has the same number, denoted r, of VLs,. Then, in, our context, VLs crossing two switches have the same distribution of end-to-end delay. Consequently, we just calculate the end-to-end delay of the VL, denoted V L 1 , with the path e 1 -S 1 -S 3 -e q .

In the following, the results presented concern the configurations of Table 1.

The Figure 5 presents the distribution of the probability P(d(0) > u) about the end-to-end delay of vl1 computed with the stochastic network calculus analysis. The Table 2 presents the upper bounds of end-to-end delay obtained by the simulation and by the stochas-tic network calculus for each network configuration (presented in Table 1. It shows that the difference between the results of simulation and stochastic network calculus increases with the load of the configuration. Consequently, the pessimism of stochastic network calculus approach increases with the load of the network.

Finally, the Figure 6 depicts the comparison between the results obtained with the stochastic network calculus, the simulation, the model checking and the deterministic network calculus for the configuration C 1 .

The model checking determines the exact worst-case end-to-end delay since it explores all possible scenarios. The result of the deterministic network calculus is higher than the result of the model checking since it considers a pessimistic upper bound on traffic. The simulation and the stochastic network calculus obtain similar worst-case end-to-end delay than the model checking. that the stochastic network calculus approach can be applied to AFDX context. The results are interesting and this method is complementary to the simulation and the deterministic network calculus. In this paper, we detail the scope of end-to-end delays analysis on an industrial switched Ethernet network for multi switches flows. Two important characteristics are analysed: the upper bound of end-to-end delays and their distribution. The first one is mandatory for certification reasons. The second one can help greatly to evaluate the pessimism of the upper bound and is valuable when prototyping the whole system. We have detailed how we apply the stochastic network calculus for multi switches flows in using the works about the existing for deterministic network calculus.

The obtained distribution of end-to-end delay is pessimistic, compared with the real behavior of the network calculated by the model checking and estimated by a simulation approach, but much less pessimistic that the upper bound obtained by a deterministic network calculus approach.

The upper bound calculated by the stochastic network calculus is near of real worst-case delay obtained by the model-checking. but we cannot compare with a load more important since it cannot be calculated by model-checcking.

In this paper we validate our method for two hop path. We must again validate our results to path with any number of switches.

Fig. 4 .

 4 Fig. 4. The network configuration Each switch output port serves the aggregate traffic (all the VLs crossing this port) with a constant rate

Fig. 5 .

 5 Fig. 5. Distribution of end-to-end delay with Stochastic network calculus The distribution of delays obtained, have higher values when the load of the network configuration increases. Thus the Delays for configuration C 1 are distributed between 233 and 241, while for the configuration C 6 , delays are mostly distributed between 1499 and 1543µs.

Fig. 6 .

 6 Fig. 6. Comparison of upper bounds of different approaches

  (t) = ρ i t + σ i ) defined in the following way. σ i is the maximum length of a frame of the VL, denoted S max . ρ i is the VL maximum flow,

	et al. (2001) and Kesidis and Kostantopoulos (2000).
	Results presented in Vojnović and Le Boudec (2002)
	and Vojnović and Le Boudec (2003) have proposed the
	tightest upper bounds.
	Vojnović and Le Boudec make the four assumptions
	presented in appendix A. The assumption (A1) im-
	poses to define a service curve for nodes. But a prop-
	erty of PSRG is that a PSRG (c, 0) implies the service
	curve β(t) = ct. Consequently, the property (A1) is
	respected. As VLs are independent at network access,
	assumption (A2) is respected. Concerning assumption
	(A3), in the AFDX context, each VL is regulated by
	a leaky-bucket (α i Smax
	BAG

The works presented by Vojnović and Le Boudec in Vojnović and Le

Boudec (2002)

and

Vojnović and Le Boudec (2003)

about networks with EF PHB service can be used to calculate the distribution of this waiting time for each switch. It is based on the probability of bound buffer overflow in the switch output port. Such a problem was previously addressed in Chang

Table 1 .

 1 Network configurations

		Simulation	Stoc. NC
	C 1	237	241
	C 2	300	487
	C 3	310	740
	C 4	372	1000
	C 5	394	1269
	C 6	399	1543

the Real-Time and Network System Conference. Poitiers, France. Frances, F., C. Fraboul and J Grieu (2006). Using network calculus to optimize the AFDX network. In: Proceedings of ERTS. Toulouse, France. IEEE 802.1D, Local and Metropolitan Area Network: Media Access Control Level Bridging. (1998). Jasperneite, Jürgen, Peter Neumann, Michael Theis and Kym Watson (2002). Deterministic Real-Time Communication with Switched Ethernet. In: Proceedings of the 4th IEEE International Workshop on Factory Communication Systems. IEEE Press. Västeras, Sweden. pp. 11-18. Kesidis, G. and T. Kostantopoulos (2000). Worst-case performance of a buffer with independent shaped arrival processes. IEEE Communications Letters. Larsen, Kim Guldstrand, Paul Pettersson and Wang Yi (1997). UPPAAL in a Nutshell. International Journal on Software Tools for Technology Transfer 1(1-2), 134-152. Le Boudec, J.Y. (1998). Application of network calculus to guaranteed service networks. IEEE Transactions on Information Theory. Le Boudec, J.Y. and P. Thiran (2001). Network Calculus: A Theory of Deterministic Queuing Systems for the Internet. Vol. 2050 of Lecture Notes in Computer Science. Springer-Verlag. ISBN: 3-540-42184-X. Ridouard, Frédéric, Jean-Luc Scharbarg and Christian Fraboul (2007). Stochastic network calculus for end-to-end delays distribution evaluation on an avionics switched ethernet. 5th International Conference on Industrial Informatics (IN-DIN 2007). Vojnović, M. and JY. Le Boudec (2002). Stochastic analysis of some expedited forwarding networks. in Proceedings of Infocom, New-York. Vojnović, M. and JY. Le Boudec (2003). Bounds for independent regulated inputs multiplexed in a service curve network element. IEEE Trans. on Communications.

Appendix A. DEFINITIONS AND ASSUMPTIONS OF VOJNOVI Ć

• let A(t) = I i=1 A i (t) be the input aggregate. • α(t) = I i=1 α i (t) denotes the aggregate arrival curve.

• ρ = I i=1 ρ i denotes the upper bound on the aggregate sustainable rate.

• τ is the intersection between the aggregate arrival curve α and the service curve β :

be the backlog at time t of a node.

• let Q(t) be an upper bound of the backlog and

Definition 1. The EF traffic inputs are homogeneously regulated, if they are regulated by the same function :

, for all i ∈ {1, . . . , I}. Otherwise, the EF traffic inputs are heterogeneously regulated.

Vojnović and Le Boudec make the following assumptions :

(A1) Nodes offer to the EF aggregate traffic, a service curve β, means that for all t (t ≥ 0), there exists s, (s ≤ t) such that

where A(t) denote (resp. A * (t)) the input (resp. the output) EF aggregate data from the node on the interval [0,t]. (A2) The EF traffic inputs are mutually independent at network ingress points.

Let A i (1 ≤ i ≤ I) be the independent EF input traffic.

(A3) Every EF input is regulated at the network ingress point. Consequently, for all i, (1 ≤ i ≤ I), there exists a wide-sense increasing function α i (called arrival curve) such that :

where A 0 i (t) represents the data observed on [0,t] of the input traffic A i at the network ingress.

for any s ≤ t where ξ i = lim t→∞ αi(t) t

Appendix B. RESULTS OF VOJNOVI Ć

Theorem 1. Homogeneous case : Assuming (A1)-(A4) and if ρ < c, for any t, the upper bound of the probability (denoted P) that the backlog is above a given level b is

for any K ∈ N, and any 0 = s 0 ≤ s 1 ≤ . . . ≤ s K = τ . where,

Corollary 1. Let a node that offers a service curve β(t) = ct and A denote the input aggregate with stationary increments and intensity ρ (ρ < c). Then, if a packet arrives in the node at time 0, it holds,

Theorem 2. For a PSRG(c, 0) node and for u ≥ 0, it is established that, if a node arrives in node at time 0, P(d(0) > u) ≤ P A (Q(0) > cu)


Bruno Fantin

Xavier Duval

Laurent Massias

Loubna Alavoine

Françoise Chau

Sylvie Retout

Fran Oise Chau

Antoine Andremont

France Mentr

-Claude Bernard

Ciprofloxacin Dosage and Emergence of Resistance in Human Commensal Bacteria

Keywords: Adult, Anti-Bacterial Agents, administration & dosage, pharmacokinetics, pharmacology, Ciprofloxacin, administration & dosage, pharmacokinetics, pharmacology, Drug Resistance, Bacterial, Escherichia coli, drug effects, Feces, microbiology, Female, Humans, Male, Microbial Sensitivity Tests, Pharynx, microbiology, Saliva, metabolism, Viridans Streptococci, drug effects, Young Adult

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Bacterial resistance to antibiotics is a growing therapeutic problem, both in the community and the hospital, involving all antibiotics including fluoroquinolones . Decreased susceptibility to fluoroquinolones arises mainly by single-step mutations in the and [START_REF] Normark | Evolution and spread of antibiotic resistance[END_REF] gyrA parC genes, which encode the fluoroquinolones targets, the topoisomerase enzymes , conferring cross-resistance to all fluoroquinolones .

[2 ] [START_REF] Chen | Decreased susceptibility of to fluoroquinolones in Canada Streptococcus pneumoniae[END_REF] Accumulation of multiple mutations in several genes confers increasing level of resistance associated with clinical failure , . [4 5 ] However, even low-level resistance can generate therapeutic failure . [START_REF] Davidson | Resistance to levofloxacin and failure of treatment of pneumococcal pneumonia[END_REF] Resistance to fluoroquinolones can result from direct selection at the site of infection or from selection in commensal bacteria followed by horizontal gene transfer to pathogens , which might even be more frequent because there are many more bacteria among [START_REF] Varon | Mechanisms and spread of fluoroquinolone resistance in Streptococcus pneumoniae[END_REF] commensal flora than within any infectious focus . In addition, differences in local antibiotic concentrations, as compared with plasma, [8 ] can affect selection of resistant bacteria in different sites , . Also, resistant commensal bacteria may be selected after any antibiotic [9 10 ] treatment, whereas resistant pathogens can emerge only in actually infected patients . [START_REF] Piddock | Fluoroquinolone resistance: overuse of fluoroquinolones in human and veterinary medicine can breed resistance[END_REF] Pharmacokinetic and pharmacodynamic parameters give rationale to antibacterial dosing , . The minimal inhibitory [12 13 ] concentration (MIC) and more recently the mutant prevention concentration (MPC) are parameters used to investigate the relationship between antibiotic exposure and efficacy or prevention of resistance development . The ratio of the area under the concentration-time [START_REF] Zhao | Restricting the selection antibiotic-resistant mutants: a general strategy derived from fluoroquinolones[END_REF] curve (AUC) to the MIC and the ratio of the peak concentration to the MIC for the infecting bacteria have been linked to treatment success with fluoroquinolones , but not to emergence of resistant pathogens, probably because the inocula at the foci of infection are [15 -18 ] limited and emergence of resistance is uncommon , . To investigate whether optimization of dosing regimens might prevent the [15 19 ] emergence of resistance in commensal flora, we studied the relationship between antibiotic pharmacokinetic and pharmacodynamic parameters in plasma, saliva and feces and the emergence of resistant strains in the pharyngeal and fecal flora in healthy volunteers receiving variable dosing regimens of ciprofloxacin, the reference fluoroquinolone.

Methods

Subjects

Eighteen to 45 year-old healthy volunteers were selected on the basis of normal findings in a thorough general examination (interview and physical examination), normal intestinal transit (one formed stool a day), normal ECG findings with a QTC < 450 ms, and normal results in a biological work-up (blood count, blood biochemistry, liver tests, urinalysis, serological tests for hepatitis viruses and HIV) [20 ] . Women of child-bering age were included if they were using effective contraception and had a negative pre-inclusion pregnancy test. The volunteers had no known allergy to a fluoroquinolone, had taken no antibacterial or antifungal drug, theophylline, steroids, vitamin K antagonists or barrier antacids during the three months before inclusion. Subjects unlikely to adhere to the study protocol, who had given blood (> 500 ml) or who had participated in another study within the previous three months were not included. Caffeine consumption was limited and stable during the two-week treatment period. Volunteers were advised to avoid exposure to sunlight throughout the treatment period. The study design was approved by the local ethics committee of Paris Bichat-Cergy Pontoise. All the participants gave their written informed consent before entering the study.

Regimens

Volunteers were randomly assigned into 6 groups of 8 individuals each, receiving either 250 mg every 12h, 500 mg every 24 h, 500 mg every 12 h, 750 mg every 24 h, 750 mg every 12h, or 1000 mg every 24 h of oral ciprofloxacin for a total of 14 days. These regimens were chosen in order to generate pharmacokinetic variability within range of clinically relevant total daily doses. Each intake was observed, and its time recorded.

Outcome and follow-up

Microbiological study

Samples

Fecal and pharyngeal samples were collected before initiation of treatment and on days 7, 14 and 42, stored at 80 C and blinded until -°analysis . Analysis focused on viridans group streptococci (VGS) in the pharyngeal flora and in the fecal flora for

[20 ]
Escherichia coli several reasons: these bacterial species are present in all subjects, they are involved in various clinical infections (bacteremia, endocarditis, urinary tract infections), and are recognized sources of horizontal gene transfer within the commensal flora. We determined for each of these target species the susceptibility to quinolones of the global population (dominant flora) and we also detected the emergence of quinolone-resistant subpopulations (subdominant flora).

Suceptibility to ciprofloxacin of the dominant flora

We used a procedure specifically designed to estimate susceptibility to fluoroquinolones of the dominant flora as a whole. Saliva samples were inoculated on colimycin-nalidixic acid (CNA) blood agar (Biom rieux, Craponne, France) and fecal samples on Drigalski é agar. After growth, we isolated ten separate colonies from each plate, identified as VGS and using standard techniques, in order to E. coli obtain a representative sample of the dominant flora. These ten colonies were mixed, and susceptibility to fluoroquinolones of the mixture was tested using minimum inhibitory concentration (MIC) in duplicate by the agar dilution method and mutant prevention concentration (MPC) in triplicate , , as described. Geometric means of these replicates were used in the analysis.

Detection of resistance in the subdominant flora

Resistance in the subdominant flora of each target bacterial species was detected by plating the fecal samples on Drigalski agar with 16 mg/L of nalidixic acid to detect first step mutant in , or containing 1 mg/L of ciprofloxacin to detect mutants resistant to E. coli ciprofloxacin. Pharyngeal samples were plated on CNA blood agar with 2 mg/L of levofloxacin because VGS are naturally resistant to ciprofloxacin but susceptible to levofloxacin . MICs of the colonies growing on selective media were determined by the agar dilution [START_REF] Mandell | Update practice guidelines for the management of community-acquired pneumonia in immunocompetent adults[END_REF] method .

[21 ]

Endpoints

Resistance to nalidixic acid and ciprofloxacin in from the fecal flora and resistance to levofloxacin in VGS from the pharyngeal E. coli flora were determined according to CLSI breakpoints . Emergence of resistance was defined by the detection of resistant strains at day [START_REF]Performance Standards for Antimicrobial Susceptibility Testing: Seventeenth Informational Supplement M100-S17[END_REF] 7, 14 or 42 in subjects in whom only susceptible strains were detected and resistant strains were not detected before treatment.

Pharmacokinetic study

Serum and saliva samples were taken from each volunteer before and 1, 3, 6 and 12 hours after the first ciprofloxacin intake, at trough on day 8 and day 14, and again 1, 3, 6 and 12 hours after the last intake . Stool samples were collected on days 0, 7, 14 and 42. All [START_REF] Darouiche | Levels of rifampin and ciprofloxacin in nasal secretions: correlation with MIC90 and eradication of nasopharyngeal carriage of bacteria[END_REF] samples were blinded and stored at 80 C until analysis. Ciprofloxacin concentrations were determined by liquid chromatography with -°fluorimetric detection after deproteinization or stool extraction in acidic medium, as described .

[25 ]

Statistical analysis

A population pharmacokinetic analysis with, as previously described a one compartment model with first order absorption [26 -28 ] was used to analyze plasma and saliva concentrations and estimate the maximal concentration (peak) and AUC from 0 to 24 h at steady-state for each volunteer, taking into account the dosing schedule. AUC/MIC, AUC/MPC, peak/MIC, peak/MPC, AUC above MIC, AUC above MPC, AUC between MIC and MPC, time above MIC, time above MPC, and time between MIC and MPC were determined using individual MIC and MPC of ciprofloxacin. In feces, concentration/MIC and concentration/MPC ratios were determined using the average of the concentrations measured at days 7 and 14.

Confidence intervals for proportion of emergence of resistance were estimated using the binomial distribution. For each target flora, the volunteers were divided into two groups (regardless of the dosing schedule) according to the emergence or not of resistance. Variables integrating pharmacokinetic and pharmacodynamic parameters were compared between the two groups using the Wilcoxon-Mann and Whitney non parametric test. Logistic regression analysis was also performed in each flora to model the link between the probability of emergence of resistance and the logarithm of AUC/MIC.

The number of subjects were determined expecting emergence of quinolone resistance in the fecal flora in one third of the volunteers [

. With this proportion and the mean AUC/MIC ratios reported previously to be significantly associated with respect to emergence 29 -31 ] of resistance at the site of infection , the power of this study was 90 with a type I error of 5 .

[32 ] % %

Results

Subjects

Eighty subjects were screened and 48 subjects (28 males and 20 females) who fulfilled the predefined criteria for healthy subjects were selected. Median age was 28.9 y range 19.5 43.9 , and median weight was 65 kg 47 93 (71 kg 53 93 in males and 55 kg 47 85 in

[ - ] [ -] [ -] [ -]
females). One subject who developed tendinitis at day 8 while receiving the 750 mg bid regimen and stopped therapy was excluded from the microbiological and pharmacokinetic follow-up analysis. The remaining 47 subjects had no treatment related side effects.

Microbiology study ( ) Figure 1

Before treatment, median range MIC and MPC of ciprofloxacin against the dominant flora were 0.016 mg/L 0.005 0.5 and 0.25

[ ] [ -]
mg/L 0.06 2.8 in the fecal flora and 2 mg/L 0.71 45.25 and 22.6 mg/L 8 512 in the pharyngeal flora, respectively. In the fecal flora,

[ -] [ - ] [ - ]
one subject had no detectable while six (13 ) initially had strains resistant to nalidixic acid, including one with resistance to both E. coli % ciprofloxacin (MIC 32 mg/L) and nalidixic acid (MIC > 1024 mg/L) and five with resistance to nalidixic acid only (MICs: 64 to > 1024 = mg/L and MICs to ciprofloxacin: 0.01 to 0.5 mg/L). All the strains resistant to ciprofloxacin were also resistant to nalidixic acid. Before treatment, in the pharyngeal flora, one subject had VGS strains resistant to levofloxacin (MIC 16 mg/L) and for one subject there was no = pharyngeal sample.

During treatment, susceptible

were not detected in the fecal flora from any volunteers. Resistance to ciprofloxacin was detected E. coli in three subjects (6 ) at day 7 and 14. By contrast, at day 42, 14 subjects [START_REF] Perea | Incidence and clinical impact of fluoroquinolone-resistant in the faecal flora of cancer patients treated with high dose Escherichia coli chemotherapy and ciprofloxacin prophylaxis[END_REF] Antibiotic concentrations and pharmacokinetic studies ( ) Figure 2 Median peak concentrations of ciprofloxacin in plasma at steady state ranged from 1.35 mg/L range: 1.13 1.77 for the 250 mg twice daily regimen to 4.26 mg/L 2.89 5.66 for the 1000 mg once daily regimen; median AUC ranged from 11.77 mg/L.h 11.56 12.08 for the

[ - ] [ - ]
250 mg bid regimen to 36.27 mg/L.h 33.23 45.49 for the 750 mg bid one. Thus, median concentrations of ciprofloxacin in plasma were

[ - ]
above median MIC against the fecal dominant flora during most of the time for all regimens, and above median MPC for all twice daily regimens. For the pharyngeal flora, median ciprofloxacin concentrations in plasma were far below median MPC and just above median MIC at peak, except for the 250 mg twice daily regimen.

Median concentrations of ciprofloxacin in stools at steady state ranged from 845 mg/L 455 1265 for the 250 mg twice daily regimen

[ - ]
to 1938 mg/L 1100 3235 for the 500 mg twice daily regimen, far above the median MIC and MPC of ciprofloxacin against the fecal

[ - ]
dominant flora. Ciprofloxacin concentrations were undetectable in stools at day 42 in all subjects.

Median peak concentrations of ciprofloxacin in saliva at steady state ranged from 0.48 mg/L 0.32 0.84 for the 250 mg twice daily

[ - ]
regimen to 1.79 mg/L 1.05 2.35 for the 1000 mg once daily one, never reaching the median MIC level of ciprofloxacin against the

[ - ]
pharyngeal dominant flora, and far below its median MPC. Ciprofloxacin concentrations were undetectable in saliva at day 42 in all subjects.

Relationship between antibiotic exposure and emergence of bacterial resistance

Distribution of AUC/MIC of ciprofloxacin in plasma, as well as ciprofloxacin concentrations/MIC ratios in feces, were not significantly different in subjects in whom resistance to nalidixic acid or ciprofloxacin emerged or not in fecal flora ( and Table 1 Figure 3 ). Other variables integrating plasma pharmacokinetic and pharmacodynamic parameters of ciprofloxacin failed to show any significant difference ( ). Logistic regression analysis did not evidence any significant link between probability of emergence of resistance in Table 2 fecal flora and antibiotic exposure as measured by AUC/MIC for ciprofloxacin in plasma or by ciprofloxacin concentrations in feces/MIC ( ). Table 1 Similar results were obtained in pharyngeal flora. Distribution of plasma AUC/MIC of ciprofloxacin in plasma or saliva did not significantly differ in subjects in whom resistance to levofloxacin emerged or not in the pharyngeal flora ( and ), nor were Table 1 Figure 3 any other variables integrating pharmacokinetic data in plasma or saliva and pharmacodynamic parameters of ciprofloxacin ( ). Table 3 Probability of emergence of resistance in pharyngeal flora was not significantly linked to antibiotic exposure measured as AUC/MIC ratio of ciprofloxacin in plasma or in saliva (

). Table 1

Discussion

We found a high rate of emergence of resistance to quinolones in commensal flora from healthy volunteers during of after a 14-day course of oral ciprofloxacin, both in fecal and pharyngeal VGS. Because this was observed in healthy volunteers, without recent E. coli antibiotic exposure, these rates are probably the minimal to be expected in patients. Indeed, higher rates of ciprofloxacin resistance, from 32 to 40 , have already been reported in fecal in cancer or leukemia patients exposed to fluoroquinolones .

% Enterobacteriaceae [28 -29 ] This can be explained by two reasons: i) antibiotic exposure of the commensal flora is more frequent in patients than in healthy volunteers and may accumulate resistance over time; ii) interpatient pharmacokinetic variability is expected to be greater in heavier, sicker and older patients from the medical wards than observed in healthy volunteers.

Emergence of resistance was mainly observed for fecal against nalidixic acid and for pharyngeal VGS against levofloxacin. E. coli Few patients developed resistance to ciprofloxacin in the fecal flora, and our study was underpowered to specifically examine E. coli differences in ciprofloxacin resistance.

Although not specifically designated to analyze time-effect relationship, our study showed that prevalences of resistance were not different between day 7 and day 14, suggesting that impact on commensal flora was already achieved at day 7 (

). Figure 1 Different kinetic patterns of emergence of the resistant bacteria were observed in the two commensal flora. Resistant strains E. coli were detected mainly 4 weeks after the end of therapy in the fecal flora while resistant VGS were primarily selected during the two weeks of therapy in the pharyngeal flora (

). Pharmacokinetic and pharmacodynamic parameters could account for these differences. In Figure 1 the feces, ciprofloxacin concentrations were very high, indeed several thousand times greater than the initial MPC on the dominant flora, explaining that virtually disappeared from the stool during therapy and that selection of resistance was unlikely. Such disappearance E. coli has previously been reported with different quinolones . It has also been shown that ciprofloxacin persists in the feces of volunteers for [START_REF] Sullivan | Effect of antibiotic agents on the ecological balance of human microflora[END_REF] several days after oral treatment ends . Therefore, resistance was probably selected in the fecal flora when ciprofloxacin [START_REF] Pecquet | Faecal excretion of ciprofloxacin after a single oral dose an dits effect on faecal bacteria in healthy volunteers[END_REF] concentrations decreased below the MPC and the MIC , . This occurred between day 14 and day 42, when no ciprofloxacin could [14 19 ] be detected in the feces anymore. In contrast, pharyngeal concentrations of ciprofloxacin during therapy were close to -but below -initial MIC level against VGS during the entire therapy, whatever the dosing regimens, explaining why resistance could be selected during treatment, and why it then decreased as antibiotic selective pressure vanished (

). Indeed, subinhibitory concentrations of Figure 1 5 10 fluoroquinolones favor selection of resistance and induce genetic transformability increasing the rate of mutation and genetic exchange in response to antibiotics , .

[19 35 ]
Depending on the target flora, we based the detection of quinolone resistance on different surrogate markers, according to their clinical relevance. Resistance to nalidixic acid, a first generation quinolone that can be prescribed for the treatment of uncomplicated urinary tract infections, was used in since it is indicative of a single first step mutation in the target gene and associated with reduced E. coli gyrA activity of fluoroquinolones . Resistance to levofloxacin was used to detect emergence of resistance in pharyngeal VGS since [29 -31 ] VGS are naturally resistant to ciprofloxacin and therefore no MIC breakpoints exist. In addition, levofloxacin is widely recommended for the treatment of respiratory infections . Emergence of resistance to levofloxacin in pharyngeal VGS obviates the selection of [START_REF] Mandell | Update practice guidelines for the management of community-acquired pneumonia in immunocompetent adults[END_REF] cross-resistance among fluorquinolones, as shown for . Streptococcus pneumoniae [START_REF] Chen | Decreased susceptibility of to fluoroquinolones in Canada Streptococcus pneumoniae[END_REF] A major issue in the use of fluoroquinolone is the role of dosing regimen to optimize efficacy. We did not identify any significant difference in antibiotic exposure in plasma, saliva and stool between subjects in whom resistance was selected or not. Similarly, the probability of emergence of resistance was comparable whatever the ciprofloxacin exposure, expressed as the ratio of the AUC to the MIC against the dominant flora. This was observed despite the fact that large ranges of ciprofloxacin dosing regimens were investigated, from the minimum to the maximum total daily dose that can be administered therapeutically. Lack of power is here unlikely and duration of treatment was sufficient to allow the selection of resistant mutants. Therefore, these results indicate that, whereas optimizing dosing regimen of ciprofloxacin is useful to increase efficacy at the focus of infection , it is not likely to be helpful to decrease the risk for

[15 -18 ]
selection of resistant strains in commensal flora. This may be explained by the different pharmacokinetic patterns of ciprofloxacin in saliva and feces as compared with the one in plasma and by the fact that variations in dosing regimens had little impact on local ciprofloxacin concentrations in saliva and in feces as compared with the respective MIC and MPC of ciprofloxacin against the dominant flora at these sites ( ). Indeed, for all ciprofloxacin regimen tested, concentrations of ciprofloxacin were always far above the MPC for Figure 2 in feces and below the MIC for VGS in saliva (

). Overall, the comparable rates of emergence of resistance in Enterobactericeae Figure 2 the fecal and pharyngeal flora whatever the antibiotic exposure suggest a random phenomenon occuring at subinhibitory concentrations (

). Thus, selection of resistant commensals during ciprofloxacin therapy should be considered as an ecological side effect which is Table 1 not preventable by optimizing antibiotic dosing. Other strategies to prevent such an event are warranted. [ ] http://www.sfm.asso.fr

Figure 1

Number of subjects harbouring strains of in fecal flora that were resistant to nalidixic acid or ciprofloxacin (top left) or strains Escherichia coli of viridans group streptococci in pharyngeal flora that were resistant to levofloxacin (bottom left) and their corresponding MIC values (mg/L) for nalidixic acid (Nal, white circles) and ciprofloxacin (Cip, black circles) (top right) and levofloxacin (bottom right) in healthy subjects receiving various dosing regimens of ciprofloxacin from day 1 to day 14. Strains that were resistant to ciprofloxacin also appear among strains resistant to nalidixic acid. There were 48 subjects at the start of therapy and 47 subjects later because of one subject discontinuing therapy. In addition, there was no pharyngeal sample to perform measurement at day 0 for one patient.

Figure 2

Mean concentration profiles of ciprofloxacin at steady state in plasma and saliva from healthy subjects receiving ciprofloxacin from day 1 to day 14, according to dosing regimens, and boxplot of the distribution of the fecal concentration at day 7 and day 14. Horizontal lines represent median MIC (mg/L) (full line) and MPC (mg/L) (dotted line) of ciprofloxacin against the dominant flora in each commensal flora.

.

  16 . Forrest A , Nix DE , Ballow CH , Birmingham MC , Cumbo TJ , Schentag JJ . Pharmacodynamics of intravenous ciprofloxacin in seriously ill patients . Antimicrob Agents Chemother . 1993 ; 37 : 1073 -81 17 . Ambrose PG , Grasela DM , Grasela TH , Passarel J , Mayer HB , Pierce PF . Pharmacodynamics of fluoroquinolones gainst against in patient Streptococcus pneumoniae with community-acquired respiratory tract infections . Antimicrob Agents Chemother . 2001 ; 45 : 2793 -7 18 . Drusano G , Preston SL , Fowler C , Corrado M , Weisinger B , Kahn J . Relationship between fluoroquinolone area under the curve: minimum inhibitory concentration ratio and the probability of eradication of the infecting pathogen, in patients with nosocomila pneumonia . J Infect Dis . 2004 ; 189 : 1590 -7 19 . Olofsson SK , Cars O . Optimizing drug exposure to minimize selection of antibiotic resistance . Clin Infect Dis . 2007 ; 45 : S129 -36 20 . Cr mieux é AC , Muller-Serieys C , Panhard X . Emergence of resistance in normal human aerobic commensal flora during telithromycin and amoxicillin/clavulanic acid treatments . Antimicrob Agents Chemother . 2003 ; 47 : 2030 -5 21 . Comit de l Antibiogramme de la Soci t Fran aise de Microbiologie January 2007 ; Communiqu du Comit de l Antibiogramme de la Soci t Fran aise de

Figure 3

 3 Figure 3 Distribution of the area under the ciprofloxacin concentration-time curve from 0 to 24 h (AUC)/MIC ratio in plasma (top and bottom left) and saliva (bottom right) and of the fecal concentrations of ciprofloxacin/MIC ratio (top right) in healthy subjects receiving various regimens of ciprofloxacin from day 1 to day 14 and in whom no resistant strains were detected at day 0. Results are presented according to the emergence or not of strains of resistant to nalidixic acid or ciprofloxacin in fecal flora (top, n 40) or of strains of viridans group Escherichia coli = streptococci that were resistant to levofloxacin in pharyngeal flora (bottom, n 45), from day 7 to day 42. The solid line represents the median=

-

  were colonized by strains resistant to nalidixic acid

	%	%
	(MICs: 64 to >1024 mg/L), including four with resistance to ciprofloxacin (MICs: 32 64 mg/L). Overall, resistance to nalidixic acid or

ciprofloxacin that was not initially detected before therapy emerged in 10/40 subjects

(25 ,

95 CI: 13 40 ), during or after therapy. % % -% In the pharyngeal flora, VGS resistant to levofloxacin were detected in eight subjects (17 ) at day 7, ten (21 ) at day 14, and four (10 % % ) at day 42. MICs of levofloxacin against the resistant strains ranged between 4 and 64 mg/L. Overall, resistance to levofloxacin that was % not initially detected before therapy emerged in 15/45 volunteers (33 , 95 CI: 20 49 ), during or after ciprofloxacin therapy. % % -%

Table 1

 1 Observed percentage of emergence of resistance in from the fecal flora and in viridans group streptococci from the pharyngeal flora in healthy volunteers according to the importance of Escherichia coli ciprofloxacin exposure expressed as quartile of the distribution. values of the nonparametric test comparing exposure in patients with or without emergence or resistance. values of the link between P P exposure and probability of emergence of resistance in logistic regression

	Parameter of ciprofloxacin exposure	No of subjects at risk	Emergence of resistance	P	values
			Number	Percent	Group comparison	Logistic regression
	Fecal flora
	AUC/MIC in plasma (h)				0.35	0.36
	361 721 -	10	2	20%
	722 1112 -	10	2	20%
	1113 2004 -	10	3	30%
	2005 4236 -	10	3	30%
	Total	40	10	25%
	Concentration/MIC in stool				0.93	0.86
	20 49 10 -× 3	10	2	20%
	50 77 10 -× 3	10	2	30%
	77 117 10 -× 3	10	3	30%
	118 358 10 -× 3	10	2	20%
	Total	40	10	25%
	Pharyngeal flora
	AUC/MIC in plasma (h)				0.86	0.27
	0.37 5.80 -	11	3	27%
	5.81 8.54 -	11	4	36%
	8.55 12.22 -	11	4	36%
	12.24 22.79 -	12	4	33%
	Total	45	15	33%
	AUC/MIC in saliva (h)				0.45	0.16
	0.06 0.87 -	11	4	36%
	0.88 1.47 -	11	4	36%
	1.48 2.21 -	11	4	36%
	2.22 6.82 -	12	3	25%
	Total	45	15	33%

Table 2

 2 Comparison of variables integrating ciprofloxacin pharmacokinetic parameters in plasma or concentrations in stool and pharmacodynamic parameters of ciprofloxacin against from the Escherichia coli dominant fecal flora between groups of subjects in whom resistant emerged or not from day 7 to day 42.

	Escherichia coli

[START_REF] Darouiche | Levels of rifampin and ciprofloxacin in nasal secretions: correlation with MIC90 and eradication of nasopharyngeal carriage of bacteria[END_REF]

[START_REF] Darouiche | Levels of rifampin and ciprofloxacin in nasal secretions: correlation with MIC90 and eradication of nasopharyngeal carriage of bacteria[END_REF]

[START_REF] Darouiche | Levels of rifampin and ciprofloxacin in nasal secretions: correlation with MIC90 and eradication of nasopharyngeal carriage of bacteria[END_REF]

[START_REF] Darouiche | Levels of rifampin and ciprofloxacin in nasal secretions: correlation with MIC90 and eradication of nasopharyngeal carriage of bacteria[END_REF]

[START_REF] Darouiche | Levels of rifampin and ciprofloxacin in nasal secretions: correlation with MIC90 and eradication of nasopharyngeal carriage of bacteria[END_REF]

Ackowledgements:

The authors thank Agn s Certain, pharmacist, for her helpful technical assistance, the study nurses Isabelle Poirier, Emmanuelle Royer and è Patricia Servant, and Pr Jean-Claude Soul , head of the gastroenterology department, who allowed the nurses of his department to supervise é the intake of ciprofloxacin on sundays (all from Bichat hospital, Paris, France).