Christoph Petersen
email: chr.petersen@tuhh.de

Maciej Muehleisen
email: maciej.muehleisen@tuhh.de

Andreas Timm-Giel
email: timm-giel@tuhh.de

Evaluation of the Aircraft Distribution in Satellite Spotbeams

Upcoming inflight entertainment and other onboard data services request broadband data connections during long-and short-haul flights all over the world. To cope with this amount of traffic, especially over oceanic areas where no ground infrastructure is available, satellite systems offer broadband satellite links for avionic purpose. This work analyzes the distribution of aircraft traffic for selected satellite spotbeams for intercontinental, rural and urban scenarios. For this, the statistic properties of the number of arriving and departing aircraft within a time interval are analyzed. Our results show, that the law of small number and therefore a Poisson distribution is only applicable to areas with low air traffic. Aircraft arrivals to-and departures from satellite spotbeams can be modeled using the negative binomial distribution, as proven by presented results.

Introduction

Aircraft are fast and popular conveyances today. For safety and passenger comfort, broadband data communication links are often installed. In some regions, but only over terrain, direct air to ground links are maintained, e.g. Aircell GoGo in the United States of America. Other avionic data links as VHF or HF do not offer high bandwidth, are highly congested and very expensive, so they are not used for services requesting high data rates. Therefore, the most widely used worldwide available avionic broadband data communication are satellite links. Fields of application range from inflight entertainment to maintenance or even flight recorder data transmission. To assess the performance of current satellite systems and estimate the capacity demands, reliable information about the number of aircraft inside specific areas are required.

In order to estimate the aggregated capacity demands, the actual offered data traffic load needs to be analyzed. It is feasible to assume the offered data traffic load being proportional to the number of aircraft in that area. Although traces of aircraft densities are available, analytical models allow more general conclusions about offered traffic loads and help to become independent from large data sets of aircraft positions. Also conclusions about areas where no aircraft position information are available may be drawn. These models are also suitable to extrapolate prospective situations or determine system performance for extraordinary situations, e.g. aviation distress. Furthermore, an analytical model can be used for systems simulation.

The same methods were applied to derive realistic vehicular traffic models. Examplarily in [START_REF] Gramaglia | New insights from the analysis of free flow vehicular traffic in highways[END_REF], a model for car arrivals on higways around the city of Madrid, Spain, is developed. The analysis of the arrival process identifies two different types of vehicles to be further investigated: Cars that drive together in a bursty way and isolated ones without any dependencies e.g. in traveling speed. Therefore, a Gaussian-exponential mixture model is proposed to handle bursty traffic with Gaussian distributed interarrival times and isolated traffic with exponential distributed interarrival times. For sparse vehicular traffic, [START_REF] Wisitpongphan | Routing in sparse vehicular ad hoc wireless networks, Selected Areas in Communications[END_REF] comes to the same result of exponential distributed vehicular interarrival times and therefore Poisson distributed vehicle arrival rates.

In [START_REF] Medina | A geographic routing strategy for north atlantic in-flight internet access via airborne mesh networking[END_REF] the German Aerospace Center (Deutsches Zentrum fuer Luft-und Raumfahrt -DLR) developed an aircraft distribution model to evaluate aircraftto-aircraft communication. In [START_REF] Medina | Feasibility of an aeronautical mobile ad hoc network over the north atlantic corridor[END_REF] the feasibility of that approach is shown, based on data from the airline flight schedule database published by the International Air Transport Association (IATA) and therefore, assuming all aircraft being equipped with ad-hoc communication equipment. The analysis presented in the following is based on more realistic aircraft position data derived from Flightradar24 1 . The available aircraft position data does not cover the whole globe. In fact, oceanic areas are very rarely covered as visible in Figure 1, showing all observed aircraft position during a two week period. Conclusions regarding aircraft densities over the ocean can be derived from aircraft position data close to the ocean shore. This is visible in Figure 2, representing the observed aircrafts with scope over the United States of America.

Aircraft Arrival Process

In order to derive worst case capacity demands, the busy hour of each day is analyzed. The area of interest for this model is a satellite spotbeam with a satellite system specific radius. Considering one particular day, the quadruple d = {lat, lon, t, id} represents one data record with the unique aircraft ID, the aircraft position in geographic coordinates lat, lon at time instance t. The set D t contains all data records worldwide at time t, whereas the subset D t,A ⊂ D is reduced to the records inside the satellite spotbeam area A, defined by a radius r around its center point lat C , lon C . Furthermore, the subset D t,A,H ⊂ D t,A describes all data records of D t,A within the given busy hour of an arbitrary day in this area. To identify the aircraft arrivals and departures, the set X t,A,H is created containing all aircraft ID records from D t,A,H of time instance t. The update interval of the captured flight data is limited to the update interval of Flightradar24 being ∆t = 10s. Therefore, a time-discrete model describing the aircraft arrivals and departures during one time instance ∆t is developed. With X t,A,H and X t+∆t,A,H as the set of aircraft for the next time instance,

a(t) = |X t+∆t,A,H \X t,A,H | (1)
is the number of aircrafts (IDs) being in that area at time instance t + ∆t but not at time instance t. Hence, a(t) is the number of aircraft arrivals in area A during that update interval. Analogously, the number of departures from the area is defined as

d(t) = |X t,A,H \X t+∆t,A,H | (2)
The data for a and d is collected and analyzed for several weeks. Figure 3 shows the distribution of aircraft arrivals inside a 200km radius of Newfoundland. It allows the hypothesis that the number of aircraft arrivals follow a Poisson distribution. This hypothesis is verified using the Chi Square test.

Scenarios

Several scenarios for the Iridium [5], [START_REF] Walke | Mobilfunknetze und ihre Protokolle 2[END_REF] low earth orbit satellite systems are further investigated. The aircraft arrival process for one spotbeam is analyzed. Depending on its position inside the overall satellite footprint, the area of the spotbeam equates to a circle becoming oval towards the border of the footprint.

In this work, a circle with radius r and according area A is assumed. The system specific radius is r Iridium = 200km for the Iridium system. The parameters for the model differ depending on the flight scenario and e.g. the used communication system. As flight scenarios, data for urban, rural or intercontinental areas is analyzed. The transition beetween these scenarios is smooth, but as typical representatives a spotbeam over New York City has been chosen for the urban scenario, over Omaha in Nebraska for the rural scenario and over the ocean shore of Newfoundland as intercontinental scenario. Aircraft arrivals in the urban scenario over New York City are not following a Poisson distribution according to the Chi Square test. The empiric distribution and the Poisson distribution with the same mean value is shown in Figure 4. Both distributions are obviously different. The Chi Square test value exceeds the critical value by far, as shown in Table 1. As the hypothesis of arrivals and departures following a Poisson distribution must be rejected, a new one is formulated. Further suitable distributions are examined with focus on generalization of the Poisson distribution. The negative binomial distribution is a generalization of the Poisson distribution with a second parameter allowing to independently select the mean and variance. The Probability Density Function (PDF) of a negative binomial distribution is stated in Equation 3

P (X = x) = p n (1 -p) x n+x-1 n-1 x ≥ 0 0 (3)
Therefore, the hypothesis for the Chi Square test is changed and the data set is tested against the negative binomial distribution. As shown in [START_REF] Hofmann | Uber zusammengesetzte poisson-prozesse und ihre anwendungen in der unfallversicherung[END_REF], the negative binomial distribution is a mixture of Poisson distributions. Whereas for the Poisson distribution hypothesis only the mean value has to be estimated, for the negative binomial hypothesis an additional estimation of the variance is needed. Hence, the degree of freedom for the Chi Square test is increased by one. As visible in Figures 5,6 The results show that inside the observed areas, the aircraft arrivals and departures follow a negative binomial distribution. It is therefore suitable to As the three investigated areas cover representative flight scenarios, it can be assumed that this model can also be applied for air traffic in other areas. Even the first assumption of poissonian aircraft arrivals remains valid since the Poisson distribution is a special case of the negative binomial distribution.

Conclusion

Aircraft position data has been collected and analyzed regarding aircraft arrivals and departures within time intervals of ∆t = 10s. The investigations focussed on an intercontinental, rural, and urban area. In all areas, the stochastical aircraft arrival process is very similar to the departure process and follows a negative binomial distribution.

In this work, we found out that the aircraft arrivals and departures inside a satellite spotbeam follow a negative binomial distribution. Future work should further clarify the reasons for this. Inside one spotbeam, especially in urban areas, arrival and departure rates of different aircraft types occur. While long range flights often just pass by, the impact of short haul flights e.g. by take off or landing is higher inside an urban spotbeam. This would also be an explanation for the varying results of the Chi Square test against the Poisson hypothesis.

For futher validation of the hypothesis more regions have to be investigated. Thereby, generally valid distribution parameter (mean value and variance) can be determined.

Fig. 1 .

 1 Fig. 1. Two weeks of captured Flightradar24 data

Fig. 2 .

 2 Fig. 2. Spotbeam over Newfoundland

Fig. 3 .

 3 Fig. 3. Observed arrivals over Newfoundland against Poisson hypothesis, r = 200km

Figure 3 Fig. 4 .

 34 Figure3shows the distribution of aircraft arrivals over Newfoundland for the intercontinental scenario as well as the theoretical distribution according to a Poisson distribution. For Chi Square testing, k classes are defined and the class number, except for the last class k, represents the number of arrivals during a time instance. The empirical rate parameter λ is set to the average number of arrivals within the considered timeframe and busy hours. The k th class summarizes the occurences of even more or equal than k -1 arrivals to avoid classes with to few arrivals.As visible in the figure, only a few aircraft pass this area. The result is based on two weeks of flight data in December 2012. The Chi Square test supports the hypothesis of aircraft arrivals being Poisson distributed with 95% confidence.

Fig. 5 .

 5 Fig. 5. Observed arrivals over Omaha against negative binomial hypothesis, r = 200km

Fig. 6 .

 6 Fig. 6. Observed arrivals over New York City against negative binomial hypothesis, r = 200km

Table 1 .

 1 and Table 2, the aircraft arrivals follow a negative binomial distribution. Overview: Chi Square test results against Poisson hypothesis

	Scenario	r Spotbeam Mean arrivals / Chi Square Critical Test
		[km]	Interval	test value value result
	Intercontinental 200 km	0,1275	3,0836	3,84 pass
	Rural	200 km	0,4052	367,82	7,82	fail
	Urban	200 km	2,49	5960	19,68 fail

Table 2 .

 2 Overview: Chi Square test results against negative binomial hypothesis assume a negative binomial for aircraft arrivals and departures in those areas.


Joachim Fabini

Michael Hirschbichler

Jiri Kuthan

Werner Wiedermann

Mobile SIP: An Empirical Study on SIP Retransmission Timers in HSPA 3G Networks

Mobile packet-switched voice must replace mobile circuitswitched voice latest with the large-scale deployment of LTE. However, short-term full-area LTE coverage is highly unlikely, handover to and interworking with 3G HSPA networks being a must. This raises the question of how the Session Initiation Protocol SIP performs in today's HSPA networks. Relying on live SIP provider monitoring data and active HSPA measurements, this paper demonstrates that default SIP retransmission timers are inappropriate for real-world deployments of packet switched voice over today's 2G and 3G networks including HSPA. Main reason for this deficiency is the reactive, demand-driven resource allocation strategy of HSPA which results in huge uplink delays. These delays eventually lead to a high number of unnecessary SIP message retransmissions which load networks and servers. SIP clients for mobile devices should therefore implement adaptive, user-configurable SIP retransmission timers and provide appropriate default values for these timers to enable seamless SIP operation in mobile cellular networks.

Introduction

From a standardization point of view, the Session Initiation Protocol (SIP) [START_REF] Rosenberg | SIP: Session Initiation Protocol Network Working Group RFC 3261[END_REF] is currently considered to be the most promising candidate for implementing Voice over IP (VoIP) in converged fixed and wireless networks. However, the SIP design and base standard is more than ten years old, being focused on providing best-effort services in deterministically behaving wired networks. During the last years, driven by requirements for deploying SIP in carrier-grade infrastructures, the research community has started to publish and discuss severe SIP deficiencies with respect to unstable behavior in high-load or overload situations.

Latest with the replacement of mobile circuit-switched voice technology with packet-switched-only capable LTE networks, IP-based signaling must operate in the mobile domain. In this paper we demonstrate by means of representative SIP server log files and measurements in state-of-the-art HSPA networks that default SIP timers as recommended by RFC 3261 are inappropriate for SIP operation in mobile 3G networks. This observation is valid for all SIP messages which are sent after seconds of inactivity, outside of ongoing data sessions, i.e., particularly for registrations and SIP presence related messages. SIP server statistics evaluations show that these SIP message types account for the majority of the overall SIP traffic. Our HSPA measurement results demonstrate that due to the highly reactive nature of HSPA uplink, timers of mobile SIP user agents will deterministically trigger SIP retransmissions, which generate redundant traffic and waste considerable resources in the network and in servers. This is a severe drawback, aggravated by the fact that mobile applications reduce user-configurable options to an absolute minimum and typically do not implement user-configurable timer values.

Related Work

The SIP protocol and SIP retransmission timers are defined in RFC 3261 [START_REF] Rosenberg | SIP: Session Initiation Protocol Network Working Group RFC 3261[END_REF], whereas SIP performance metrics for registration request delay are standardized in RFC 6076 [START_REF] Malas | Basic Telephony SIP End-to-End Performance Metrics Network Working Group RFC 6076[END_REF]. C. Egger et. al. discuss in [START_REF] Egger | Leistungs-, Zuverlaessigkeits-und Verlaesslichkeitsbewertung von Kommunikationsnetzen und verteilten Systemen[END_REF] and [START_REF] Egger | Collapse Detection and Avoidance for SIP Architectures[END_REF] the inherent problem of SIP retransmissions and their negative impact on SIP proxy performance and networks, proposing to manipulate SIP retransmission timers to handle SIP overload situations. The authors of [START_REF] Happenhofer | Hirschbichler An Architectural and Evaluative Review of Implicit and Explicit SIP Overload Handling[END_REF] conclude that SIP overload control mechanisms are an absolute MUST, implicit overload control being subject to lower overhead but explicit overload control behaving more deterministic in situations of high overload. Vingarzan et. al. discuss in [START_REF] Vingarzan | End-to-end performance of the IP multimedia subsystem over various wireless networks[END_REF] the latency impact of various wireless network technologies, including 2G, 3G, and WiFi onto end-to-end SIP performance for IMS, concluding that GPRS networks are not appropriate for IMS signaling, whereas IEEE 802.11b,g, and CDMA networks can handle IMS traffic adequately in terms of delay and loss. The contribution of different network components (user equipment, NodeB and RNC) on HSUPA end-to-end delay is analyzed in [START_REF] Laner | Dissecting 3G Uplink Delay by Measuring in an Operational HSPA Network[END_REF], inferring on 30 ms delay for 1 kbyte packets. In earlier work ( [START_REF] Fabini | The Illusion of Being Deterministic -Application-Level Considerations on Delay in 3G HSPA Networks[END_REF] and [START_REF] Fabini | The Importance of Being Really Random: Methodological Aspects of IP-Layer 2G and 3G Network Delay Assessment[END_REF]) we have dissected difficulties and uncertainty factors to be expected when measuring mobile network delay, focusing on randomness in terms of inter-packet delay and payload size as key factor to reveal load-dependent network behavior.

Structure of this Paper

The remainder of this paper is structured as follows: section 2 reviews the SIP registration procedure and discusses the methodology used for iptel.org SIP registrar log evaluation and for HSPA measurements. Building on this information, section 3 presents and discusses SIP registrar log and measurement results from live HSPA networks. The paper ends with summary and conclusions in section 4.

Protocols and Setup

Adoption of SIP by the 3rd Generation Partnership Project (3GPP) as main signaling protocol for the IP Multimedia Subsystem (IMS) has significantly boosted the world wide use of SIP. Due to high scalability and freely available standards, several free, open-source SIP client and server implementations are available for download. In the following we restrict discussions to plain SIP registration, arguing that 3GPP SIP signaling messages are typically larger than plain SIP signaling messages because of 3GPP-specific SIP extensions and headers. Therefore, delays are likely to increase for 3GPP IMS signaling even more, plain SIP delays offering a lower boundary on propagation delays in mobile networks. Even if SIP signaling compression is deployed as mandated by 3GPP for the use on wireless cellular networks, compression is unlikely to offer significant delay reductions for sporadically sent messages like SIP registrations.

SIP Basics: Registration

SIP is a simple, plain-text message based request-reply protocol. Fundamental to SIP is the registration process. During registration a terminal, the so-called SIP user agent, registers the user's generic SIP address -the so called SIP URIand its current transport address with its assigned SIP server, the SIP registrar. Using the transport address binding stored during the user's registration process, SIP registrars can then forward incoming calls via IP routing to the terminal(s) where the specific user is currently logged in. 1) is rejected by the registrar using a 401, unauthorized reply (2). This reply message includes a random value, the so-called nonce, which is encrypted by the user agent on receiving the reply using a secret key shared with the registrar. This response is appended as SIP authentication header to a new registration request (3) sent to the registrar. On receiving the authenticated registration request, the registrar repeats the user agent's processing, i.e., encodes the random value with its pre-shared secret. If the result matches the response sent by the user agent in its registration request, the registering user is supposed to be authenticated. The registrar can safely store the binding between the client's SIP URI and its contact (transport) address and confirm successful authentication to the client by sending a 200 OK response (message 4 in fig. 1).

Registrations expire, raising the need for periodical registration message retransmissions to refresh the registration state. The interval between successive re-registrations is always a trade-off between the user agent's reachability for incoming calls, i.e., up-to-date registrar information, and the amount of required signaling load. In a mobile cellular context, mobility and radio provisioning are two factors which can result in IP address changes and therefore demand for relatively small registration intervals. Moreover, mobile firewalls and/or private IP address NAT devices in some cases use these re-registrations as keep-alive messages to maintain their internal bindings. Consequently, re-registration intervals for mobile SIP clients should be in the order of tens of minutes, compared to wired SIP terminals which typically re-register every hour or several hours. However, this high registration frequency causes a high data volume for SIP over mobile networks.

SIP Registrar Logging

iptelorg GmbH offers free SIP-based IP Telephony services. Users can request their free personal SIP URI @iptel.org and use this URI to register their SIP user agents with the SIP registrar iptel.org. The core functionality behind the iptel.org registrar is implemented by the open source SIP Express Router (SER)[14], which offers complex and detailed logging facilities. The results published in this paper base on 27 hours of anonymized, representative iptel.org SER logs acquired during a typical business day in spring 2012. During these 27 hours, the log has recorded a total of 9,980,000 SIP requests including retransmissions which scales down to an effective traffic of 7,400,000 SIP requests and 7,500,000 SIP replies when eliminating SIP message retransmissions. Prior to evaluation, all SIP messages have been categorized into several orthogonal classes, focusing on the SIP registration process.

First, all SIP requests have been categorized according to their type. A second category differentiates between the user agent classes "fixed" and "mobile" by comparing logged SIP User-Agent headers against a list of well-known user agent strings. Subclass "mobile" aggregates smartphone clients, i.e., software SIP clients for iOS and Android which might face limitations in terms of computing ressources. However, "mobile" does not infer on any specific kind of network connectivity, on the contrary. One of our conclusions in this paper is, that the majority of these mobile clients connect using Wireless LAN networks rather than using cellular technologies. As second option, the subclass "fixed" groups hard-phones, SIP-routers and -proxies, as well as soft-phones for desktop operating systems which typically have abundant ressources available.

Table 1 summarizes the SIP registrar log, classifying SIP requests according to their request type for fixed clients (Fixed ), mobile clients (Mobile), and aggregated (Total ), considering only first requests (i.e., eliminating all retransmissions). Registrations dominate this statistic, accounting for more than 40% of all requests (3,090,000 registrations in absolute numbers). This confirms our assumption that SIP registration requests generate significant load in mobile and fixed networks. However, in a server-based enterprise infrastructure featuring server-based presence services we predict a load shift towards notify and subscribe requests. As third category, because of their distinct handling and response time within the SIP registrar, SIP registration requests must be divided into registrations without authentication information (message 1 in fig. 1) and registrations with authentication information (message 3 in fig. 1). More, detailed registration request statistics can be found in the following measurement results section.

HSPA Measurement Setup

For measuring one-way (OWD) and round-trip delay (RTD) in mobile cellular networks we have used operational High Speed Packet Access (HSPA) networks. connected using its on-board Ethernet interface to the public Internet. The mobile client is a Dell Latitude D630 laptop with an Intel T7100 processor at 1.8 GHz and 2 Gbyte of RAM, connected to the mobile network using a Huawei E870 HSPA ExpressCard 34. For accurate OWD measurements, mobile client and server are both time-synchronized using the network time protocol daemon (NTPD) and local EM 406A based GPS-PPS time sources as recommended by [START_REF] Laner | Time Synchronization Performance of Desktop Computers[END_REF]. The maximum measured deviation from global time is below 50 µs, which is sufficiently accurate for our measurements. From a measurement methodology point of view we have followed and extended the recommendations of the IP Performance Metrics Framework [START_REF] Paxson | Framework for IP Performance Metrics Network Working Group RFC 2330[END_REF] to avoid correlation with periodic network behavior. The measurement traffic is random with respect to send time and payload size. ICMP echo request packets of representative random payload size are sent at random time intervals, triggering corresponding ICMP echo replies.

Measurement Results

This section presents the iptel.org SIP server log analysis and HSPA delay measurement results for sporadic SIP registration traffic designed according to the iptel.org log evaluation. As main criterion for representativeness we have used the live traces from iptel.org, such that the packet size of our measurement traffic matches the size of real registration messages.

SIP Registrar Statistics

As mentioned in subsection 2.2, the monitored SIP traffic totals 27 hours of traffic. Out of the 7.4 million unique SIP requests 4.6 million requests are from fixed clients and 2.8 million from mobile clients conforming to the mobile-fixed categorization presented in section 2.2. Table 2 transmit SIP registration requests almost three time as frequent as fixed clients.

In average, every fifth register request is retransmitted due to firing of SIP retransmission timer T1 (500 ms). Retransmission messages are evenly distributed over all mobile clients and request sizes, which excludes that this problematic behavior is initiated by one specific user or user-agent implementation. It must be emphasized once again that "mobile" client is NOT a synonym for 3G connectivity. On the contrary, more detailed iptel.org log evaluation indicates that the majority of mobile clients connects using WLAN or faster non-3G technologies. To eliminate SIP server or core network performance as potential delay sources we have evaluated processing duration of SIP registration requests with and without authentication. Using metrics from [START_REF] Malas | Basic Telephony SIP End-to-End Performance Metrics Network Working Group RFC 6076[END_REF], nearly 99% of all "401 Unauthorized" responses are sent within 1 ms and 98% of all "200 OK" within 2 ms of registration request arrival. Both values are well below the SIP retransmission timer T1 value of 500 ms, such that SIP server delay can be excluded as reason for timer T1 expiry.

HSPA Measurement Results

Based on the evaluation of iptel.org's SIP server log we have built a prototypical signaling data stream at IP layer using ICMP messages to measure accurate round-trip (RTD) and one-way uplink (UL) and downlink (DL) delay measurements for SIP signaling traffic in live HSPA networks. Main motivation of these HSPA delay measurements was to determine the impact and feasibility of VoIP on top of mobile HSPA networks. HSPA was selected as mobile cellular technology because back in Q2 2012, when acquiring iptel.org traces for this publication, no LTE capable terminals have been available on the market. Therefore it is unlikely that mobile clients have accessed iptel.org in spring 2012 using a more advanced technology than HSPA. Today, one year later, Long Term Evolution (LTE) networks are operational in many countries worldwide but typically still limited in their coverage to high-traffic areas.

Using the setup presented in section 2, an extended Internet Control Message Protocol (ICMP) packet generator and an artificial, random signaling data traffic we have measured end-to-end RTD and OWD in public live Austrian HSPA networks. As mentioned earlier, measurement representativeness has been increased by following the recommendations of the IPPM Framework [START_REF] Paxson | Framework for IP Performance Metrics Network Working Group RFC 2330[END_REF] and of its associated metrics for OWD [START_REF] Almes | A One-way Delay Metric for IPPM Network Working Group RFC 2679[END_REF] and RTD [START_REF] Almes | A Round-trip Delay Metric for IPPM Network Working Group RFC 2681[END_REF] when designing the measurement traffic. In particular we have created a scenario consisting of 10,000 single ICMP measurement packets. Based on iptel.org log's payload size distribution for mobile clients as depicted in fig. 3(b), the measurement traffic's payload range is uniform distributed between 400 and 800 byte. The measurement traffic's interpacket interval is uniformly distributed between 1 and 10 seconds, totaling more than 15 measurement hours. The selected delay range has been chosen as a minimum period of mobile network inactivity. We argue this period to be exceeded in most cases for registration requests while the terminal is idle, i.e., has no ongoing packet-switched voice or data sessions.

Figure 4 shows the resulting diagrams and statistics for RTD measurements. The x-y scatter plot in fig 4(a) depicts delay as a function of payload size. Any one of the almost 10,000 dots in the figure correspond to the delay value of one single measurement packet. Only 3 packets out of the 10,000 were lost, meaning that loss can be excluded for the large number of retransmission of mobile clients. The corresponding cumulative distribution function (CDF) in fig 4 (c) reveals that -ignoring potential processing overhead and delay in SIP Registrars -slightly more than one third (36.2%) of all measurement samples arrive in less than 500 ms. Accordingly, almost two thirds (63.8%) of the requests will trigger retransmissions. More than 10% of all requests will exceed 1500 ms and trigger at least two retransmissions.

As mentioned earlier in section 2.1 SIP re-registrations must be sent periodically. We argue that there is a high likelihood that intervals of mobile network inactivity preceding a SIP Registration are significantly larger than one second. We have therefore selected from all 10,000 measurement samples the 5441 ones which have inter-packet delays -i.e., network inactivity period before sending the packet -between 5 and 10 seconds. The result is alarming with respect to user experience, network load and server load. Considering exclusively network delay, less than 4% of all mea- surement samples arrive within the expected timeframe of 500 ms to avoid SIP retransmissions. More than 96% of all SIP requests will therefore trigger at least one, 8% will exceed the default limit of 1500 ms and trigger at least two retransmissions. These results show that in a passive state with no ongoing call, mobile SIP devices on HSPA networks will effectively -at least -double the effective load on the network and on the registrar. Although resource allocation andrelease in HSPA networks depends significantly on operator-specific parameters, measurements in other mobile HSPA networks suggest that the figures we have obtained are relevant with respect to the order of magnitude. It is important to note that these findings are not restricted to Voice over IP but can be generalized for other SIP-based services as Presence or Instant Messaging, too, which all use the default timer T1 value of 500 ms.

For isolating an accurate origin of the large RTD we have dissected measured round-trip-delay samples into UL and DL delay as displayed in fig 5 . The figures confirm that the major delay uncertainty factor is HSPA UL. The reason for the high end-to-end delay experienced by a mobile client following a period of network inactivity is intrinsic to HSPA's architecture. Mobile clients must send signaling messages over the wireless link to the network-based scheduler to switch from inactivity or to request allocation of additional capacities in the wireless network. These round-trip messages delay the sending of first messages, whereas subsequent messages can be transmitted much faster due to already allocated capacities.

Comparing one-way UL delay diagrams for 1-10 s inter-packet delay in The DL delay depicted in fig. 5(c) and 5(f) recovers much faster from inactivity. On DL data arrival the scheduler is located in the wired network domain and can act instantaneously, which saves time-consuming round-trip signaling messages over the wireless link. More than 80% of DL samples are below 50 ms and more than 90% below 200 ms end-to-end delay

Discussion

Two main factors may originate SIP retransmissions: mobile client limitations in terms of software and hardware or reactive HSPA UL behavior. Diving deeper into iptel.org's server log details reveals that a) mobile client limitations can be one main reason for increased retransmission ratio on iptel.org and b) as of today few mobile clients use 2G or 3G technologies to connect to iptel.org. These statements can be concluded from table 3 which shows SIP retransmission ratio depending on a presumed mobile link state. Based on the finding of section 3.2 that HSPA clients experience an increased delay after more than 5 seconds of network inactivity, mobile client registrations have been split into two categories. A mobile client's network connection is supposed to be active when iptel.org has logged a message from the client's socket within 5 seconds before arrival of the request, or inactive otherwise.

Comparing total registration request retransmission ratio for mobile clients with and without authentication in table 3 reveals that more register requests

Summary and Conclusions

The aggregated finding of SIP server log analysis and HSPA delay measurements is that large-scale deployment and operation of default-configured mobile SIP clients will put today's HSPA networks at risk. As main conclusion of iptel.org SIP server log and HSPA measurement results we recommend all mobile SIP clients to offer user-configurable SIP retransmission timer values. The application-configured default values for HSPA networks must be at least double of the default SIP timer T1 value of 500 ms, i.e. 1 second. For a detailed discussion on retransmission timer effects and fine-tuning we refer the reader to [START_REF] Egger | Leistungs-, Zuverlaessigkeits-und Verlaesslichkeitsbewertung von Kommunikationsnetzen und verteilten Systemen[END_REF]. Alternatively, SIP clients could ideally support automated, mobilenetwork-technology-dependent values for T1. Using cross-layer information on the network technology which the mobile device currently uses (e.g., WiFi or 3G), mobile SIP clients could configure appropriate SIP timer values to minimize the likelihood of unnecessary retransmissions. Latest with large-scale deployment of SIP clients in mobile cellular networks, network and SIP server operators will be forced to over-dimension their infrastructure by orders of magnitude and to implement SIP overload control mechanisms. The authors of [START_REF] Egger | Collapse Detection and Avoidance for SIP Architectures[END_REF] have demonstrated the catastrophic impact that shortterm SIP network overloads can have onto network stability. A SIP retransmission flooding triggered by a short-term overload period eventually can end up in a congestion collapse state for SIP servers and networks. Recovery from SIP congestion collapse requires appropriate algorithms and substantial load reduction. For safeguarding acceptable user experience of SIP in mobile cellular networks it is highly desired to prevent congestion collapse scenarios, adequate SIP timer handling being a first, mandatory step.

Fig. 1 .

 1 Fig. 1. SIP Registration message flow

Fig. 1

 1 Fig.1illustrates the message sequence required for an authenticated SIP registration. The first registration request (1) is rejected by the registrar using a 401, unauthorized reply (2). This reply message includes a random value, the so-called nonce, which is encrypted by the user agent on receiving the reply using a secret key shared with the registrar. This response is appended as SIP authentication header to a new registration request (3) sent to the registrar. On receiving the authenticated registration request, the registrar repeats the user agent's processing, i.e., encodes the random value with its pre-shared secret. If the result matches the response sent by the user agent in its registration request, the registering user is supposed to be authenticated. The registrar can safely store the binding between the client's SIP URI and its contact (transport) address and confirm successful authentication to the client by sending a 200 OK response (message 4 in fig.1).

Fig. 2 .

 2 Fig. 2. Measurement Setup for Accurate OWD Measurements

Fig. 2

 2 Fig. 2 depicts the setup used for active end-to-end delay measurements in public HSPA networks. Measurement server and mobile terminal are both running Ubuntu Linux 12.04 using a custom-compiled Kernel 3.4.0 at 1 kHz kernel tick with Pulse-per-second (PPS) functionality activated. The measurement server is equipped with an Intel Q6600 CPU at 2.4 GHz and 4 Gbyte of RAM,

( a )Fig. 3 .

 a3 Fig. 3. SIP REGISTER size distribution with and without authentication header As presented in section 2.1 in fig. 1, an authenticated SIP registration requires two SIP register requests. The second request (message 3) differs from the first one (message 1) by the additional SIP authentication header. Fig. 3(a) and fig. 3(b) show the distribution of SIP register request size with and without authentication header for fixed and mobile clients, respectively. Accordingly, the authentication header is increasing SIP request size in average by about 200 bytes.To eliminate SIP server or core network performance as potential delay sources we have evaluated processing duration of SIP registration requests with and without authentication. Using metrics from[START_REF] Malas | Basic Telephony SIP End-to-End Performance Metrics Network Working Group RFC 6076[END_REF], nearly 99% of all "401 Unauthorized" responses are sent within 1 ms and 98% of all "200 OK" within 2 ms of registration request arrival. Both values are well below the SIP retransmission timer T1 value of 500 ms, such that SIP server delay can be excluded as reason for timer T1 expiry.

  The resulting scatter plot is depicted in fig 4(b) and the distribution function in fig 4(d), respectively.

Fig. 4 .

 4 Fig. 4. RTD dependence on inter-packet send interval for HSPA networks.

  fig 5, left (5(a) and 5(d)), with the corresponding diagrams with larger inter-packet delay of 5-10 s shown in fig 5, center (5(b) and 5(e)), reveals that the ratio of requests which unconditionally run into SIP retransmission timeouts increases to more than 90% after more than 5 seconds of inactivity.

Fig. 5 .

 5 Fig. 5. UL and DL delay dependence on inter-packet send interval for HSPA networks.

Table 1 .

 1 SIP request distribution (no retransmissions)

	Request	Total Fixed Mobile
	INVITE	0.19% 0.29% 0.03%
	BYE	0.05% 0.08% 0.01%
	REGISTER 41.50% 51.45% 25.39%
	SUBSCRIBE 2.77% 3.46% 1.65%
	NOTIFY	17.81% 28.82% 0.001%
	OPTIONS	37.22% 15.21% 72.85%
	Others	0.46% 0.70% 0.07%

Table 2 .

 2 illustrates that mobile clients re-Total register requests vs. registrations which require retransmission

		Register Requests Register Requests Ratio
			w Retransmissions
	Fixed	2,365,404	167,467 7.08%
	Mobile	721,303	161,111 22.34%

Table 3 .

 3 Register request retransmission probability depending on load history with authentication are retransmitted than without. This result conflicts with our HSPA delay measurement results, where 96% of requests sent with inactive mobile network are retransmitted but only 63% of the active ones. Combined with the relatively low retransmission ratio for iptel.org we argue that the majority of clients connect using WiFi or alternative non-cellular technologies. RTD of WiFi networks is typically below 10 ms, such that time-consuming parsing of SIP messages by the mobile client contributes to the retransmission count.

	Connection	Ratio	Ratio Ratio
		(total) (inactive) (active)
	Fixed (w/o auth.)	7.95%	8.65%	6.07%
	Fixed (w auth.)	3.63%	0.00%	4.10%
	Mobile (w/o auth.) 18.70%	11.95% 45.11%
	Mobile (w auth.)	24.34%	0.00% 24.46%

Acknowledgment

The authors would like to thank their colleagues Markus Laner and Philipp Svoboda for their work and support in implementing reliable, affordable solutions for accurate GPS-PPS based measurement clock synchronization. The views expressed in this paper are those of the authors and do not necessarily reflect the views of their employers.