In two-hop ad hoc networks the available radio capacity tends to be equally shard among the contending stations, which may lead to bottleneck situations in case of unbalanced traffic routing. We propose a generic model for evaluating adaptive capacity sharing strategies. We use infinite-state stochastic Petri nets for modeling the system and use the logic CSRL for specifying the measures of interest

Cloth, L.

Haverkort, B.R.

Remke, A.

English

Remke, Anne

Haverkort, Boudewijn R.

Cloth, Lucia

University of Twente Research Information

Bottlenecks in Two-Hop Ad Hoc NetworksDividing Radio Capacity in a Smart WayA. Remkea, B.R. Haverkorta, L. Clothaa Design and Analysis of Communication Systems,University of Twente,[anne,brh,lucia]@ewi.utwente.nlAbstractIn two-hop ad hoc networks the available radio capacity tends to be equally shared amongthe contending stations, which may lead to bottleneck situations in case of unbalanced trafficrouting. We propose a generic model for evaluating adaptive capacity sharing strategies. Weuse infinite-state stochastic Petri nets for modeling the system and use the logic CSRL forspecifying the measures of interest.1 IntroductionThe availability of cheap yet powerful wireless access technology, most notably the IEEE802.11 (“wireless LAN”), has given an impulse to the development of wireless ad hoc networks.In such networks, the stations (nodes) that are in reach of each other, facilitate connectivity byforwarding traffic, e.g., to obtain access to the fixed internet. In an 802.11 ad hoc network, thestations that are in mutual reach, help each other in obtaining and maintaining connectivity.At the same time they are also competitors, as they all contend for the same resource, i.e.,the shared ether as transmission medium. The medium access control of 802.11 is basedon CSMA/CA and is commonly referred to as the distributed coordination function (DCF)[1, 2]. Research has shown that, effectively, the DCF tends to equally share the capacityamong contending stations, thus leading to a processor sharing type of scheduling [3, 5].Although this appears to be a nice fairness property, this fairness may lead to undesirablesituations in case one of the nodes happens to function as a bridge toward either anothergroup of nodes, or to the fixed internet as illustrated in Figure 1, in such cases of unbalancedtraffic routing.2 Earlier workEarlier work on the performance of IEEE 802.11 ad hoc networks considers a variety ofscenarios, cf. [6], however, none of the papers mentioned there, explicitly addresses thedelays or throughputs in a multihop ad hoc network. In [6], a two-hop ad hoc network isconsidered, where the second hop has to forward the traffic of many sources (the first hops),thus forming a bottleneck, since all active stations have to share the transmission capacity.[6] yields explicit (closed-form) equations for the expected overall delay and the expecteddelay at the bottleneck, by translating the model at hand into a generalized processor sharingqueuing model, as studied by Cohen [7]. Although the analysis is approximate, good resultsare obtained, as confirmed by simulations. However, this evaluation approach is limited inthat it only allows for an equal sharing of transmission capacity between active stations.A. Remke, B.R. Haverkort, L. Clothbottleneck BinternetFigure 1: Wireless ad hoc network connected to the fixed internet3 Our recent workWe follow the same line of modeling as in [6], however, we allow for alternative capacitysharing strategies as well; such strategies are made possible through the recent QoS-extensionof the IEEE 802.11 standard, e.g., through the EDCA (“E”) version [8]. In doing so, we canstudy the impact of adaptive capacity sharing strategies that recognize potential bottlenecksand adapt accordingly.In [10] we already modeled and analyzed two alternative capacity sharing strategies. Toachieve flexibility in modeling and at the same time more modeling convenience, we specifiedour models as infinite-state stochastic Petri nets (iSPNs) [9]. The underlying infinite-stateMarkov chain, which can be automatically generated from the iSPN, then obeys a quasi-birth-death (QBD) structure [9]. Equipping these QBDs with rewards and using the logic CSRL(continuous stochastic reward logic [11]) to specify measures, we analyzed these alternativecapacity sharing strategies using new model checking algorithms for CSRL on QBDs. Thetwo adaptive capacity sharing strategies as analyzed in [10] are the so-called buffer-relatedthreshold (BRT) and source-related threshold (SRT).The BRT model distinguishes two modes: in the low occupancy mode the buffer contentis less than a given value τ and the bottleneck node and each active source receives an equalshare of the radio capacity C. BRT enters the high occupancy mode whenever there are atleast τ packets waiting in the buffer. The bottleneck node then receives 50% of the radiocapacity and all active sources equally share the remaining 50%.SRT distinguishes three modes: in the start up mode, when less then m sources are active,the bottleneck node and each active source receives an equal share of the radio capacity. Assoon as at least m sources are active, SRT enters the run mode and the bottleneck nodereceives m times as much radio capacity as every single active source. When the number ofactive sources drops again below m, SRT enters the clearance mode where the allocation ofradio capacity stays the same as in the run mode, to assure that the buffer will be emptiedcompletely. When the buffer is completely empty, SRT switches back to start up mode.4 A framework for adaptive capacity sharing modelsModeling adaptive capacity sharing strategies as QBDs provides more flexibility than thathas been explored in [10]. In essence, our modeling approach allows us to specify and analyzea whole range of adaptive capacity sharing strategies, that can be characterized along threeA. Remke, B.R. Haverkort, L. Clothdimensions:1. The number of modes specifies how many different allocation regimes will be distin-guished.2. A corresponding number of threshold values specifies when a change of operational modelis in place. Furthermore, it should be specified whether the threshold is to be reachedfrom above or below, and whether it is buffer- or source-related.3. We have to decide on a resource allocation in the different modes.The earlier models we proposed, i.e., BRT and SRT, as well as the original processor sharingmodel are special cases of the above. The above approach allows, however, for more generalsharing techniques. The number of modes is, in principle, unlimited, however, distinguishingfew modes only does well in practice. Furthermore, in case of even more modes, selecting thethreshold values and radio capacity allocation shares will be a more difficult problem (toomany combinations possible to sensibly choose from).From our study [10], it appears that an allocation of half of the radio capacity to thebottleneck and the other half to the active sources is very fair: it benefits the bottleneck andhas little impact on the number of active sources. It will be interesting to combine this fixedresource allocation with a source-related threshold and to study whether there are still betterfixed resource allocations. As our work on the SRT model has shown [10], such adaptivecapacity sharing strategies are not easy to understand and their performance can be rathercounter-intuitive. Thus, evaluating a wide variety of adaptive capacity sharing strategiesseems to be essential to come up with an effective design.The model specification (as above) is done separately from the specification of the mea-sures of interest; for the latter purpose we use the logic CSRL. In doing so, it is straightforwardto compute the packet length distribution in the bottleneck station, the fraction of time spentin the various modes, as well as the distribution of the amount of work done (the numberof packets handled by the bottleneck) in a given interval of length t. The general modelchecking procedure that we advocate allows us to compute these measures almost completelyautomatically.Model checking CSRL formulas for the mentioned measures relies on algorithms for thecomputation of the steady-state probabilities, the transient probabilities, the expected rewardand the distribution of the accumulated reward. The most involved algorithms are requiredfor the accumulated reward distribution: they have a time complexity that is cubic in thenumber of considered QBD states and grows at least quadratically with increasing accuracy[4].In the final paper (and workshop presentation) we will present a variety of (new) capac-ity sharing models and evaluate their (relative) performance, from which we conclude withrecommendations for future capacity sharing techniques in ad hoc networks.Bibliography[1] J. Kurose and K. Ross, Computer Networking. Addison-Wesley, 2005.[2] J. Schiller, Mobile Communications. Addison-Wesley, 2003.A. Remke, B.R. Haverkort, L. Cloth[3] G. Bianchi, “Performance analysis of the IEEE 802.11 Distributed Coordination Func-tion,” IEEE Journal on Selected Areas in Communications 18: 535–547, 2000.[4] L. Cloth and B. R. Haverkort.”Five performability algorithms: A comparison.” MarkovAnniversary Meeting: 39–54. Boson Books, 2006.[5] R. Litjens, R. Roijers, J.L. van den Berg, R. Boucherie, and M. Fleuren, “Analysis offlow transfer times in IEEE 802.11 wireless LANs,” Annals of Telecommunications 59:1407–1432, 2004.[6] J.L. van den Berg, M. Mandjes, and F. Roijers, “Performance modeling of a bottlenecknode in an IEEE 802.11 ad-hoc network,” in ADHOC NOW, 2006.[7] J. Cohen, “The multiple phase service network with Generalized Processor Sharing,”Acta Informatica 12: 245–284, 1979.[8] IEEE 802.11e/D13.0, “Wireless LAN Medium Access Control (MAC) and Physical layer(PHY) specifications: Medium Access Control (MAC) Enhancements for Quality of Ser-vice (QoS),” draft supp. to IEEE 802.11 std., 2005.[9] A. Ost, Performance of communication Systems. Springer, 2001.[10] A. Remke, B.R. Haverkort, and L. Cloth, “A versatile infinite-state Markov reward modelto study bottlenecks in 2-hop ad hoc networks,” in QEST ’06 : 63–72. IEEE ComputerSociety: , 2006.[11] C. Baier, B. R. Haverkort, H. Hermanns, and J.-P. Katoen, “On the logical characteri-sation of performability properties,” LNCS 1853: 780–792, 2000.

Bottlenecks in Two-Hop Ad Hoc Networks - Dividing Radio Capacity in a Smart Way

A versatile inﬁnite-state Markov reward model to study bottlenecks in 2-hop ad hoc networks,”

Analysis of ﬂow transfer times

Computer Networking.

Haverkort.”Five performability algorithms: A comparison.”

Mobile Communications.

On the logical characterisation of performability properties,”

Performance analysis of the

Performance modeling of a bottleneck node in an

Performance of communication Systems.

The multiple phase service network with Generalized Processor

Wireless LAN Medium Access Control (MAC) and Physical layer (PHY) speciﬁcations: Medium Access Control (MAC) Enhancements for Quality of Service (QoS),” draft supp. to IEEE 802.11 std.,

http://purl.utwente.nl/publications/66704

Bottlenecks in Two-Hop Ad Hoc Networks - Dividing Radio Capacity in a Smart Way

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