A diffusion approximation model for wireless networks based on IEEE 802.11 standard Tadeusz Czachórski a, * , Krzysztof Grochla a , Tomasz Nycz b , Ferhan Pekergin c a Institute of Theoretical and Applied Informatics of Polish Academy of Sciences, Baltycka 5, 44-100 Gliwice, Poland b Silesian University of Technology, 44-100 Gliwice, Poland c LIPN, Université Paris-Nord, 93430 Villetaneuse, France article info Article history: Available online 15 July 2010 Keywords: Diffusion approximation Queueing network models Distributed coordination function CSMA/CA IEEE 802.11 protocol abstract The article presents an analytical model of wireless networks using the IEEE 802.11 protocol to access the transport medium. The model allows to determine such key factors of the quality of service as transmis- sion delays and losses. The model is based on diffusion approximation approach which was proposed three decades ago to model wired networks. We show that it can be adapted to take into consideration the input streams with general interarrival time distributions and servers with general service time dis- tributions. The diffusion approximation has been chosen because of fairly general assumptions of models based on it, hard to be represented in Markov models. A queueing network model can have an arbitrary topology, the intensity of transmitted flows can be represented by non-Poisson (even self-similar) streams, the service times at nodes can be defined by general distributions. These assumptions are impor- tant: because of the CSMA/CA algorithm, the overall times needed to sent a packet are far from being exponentially distributed and therefore the flows between nodes are non-Poisson. Diffusion approxima- tion allows us also to analyse the of transient behaviour of a network when traffic intensity is changing with time. Ó 2010 Published by Elsevier B.V. 1. Introduction The traffic transmitted by wireless networks has become more and more important, hence the performance and QoS issues of these networks should be carefully studied. The performance of IEEE 802.11 standard for wireless networks, its Carrier Sense Mul- tiple Access with Collision Avoidance (CSMA/CA) scheme with exponential backoff mechanism and its variants used to support asynchronous transfers, were thoroughly studied either analyti- cally or by simulation e.g. in [1,15,4,2,21,25,26]. The studies usu- ally refer to the limit high traffic conditions. The relationships among throughput, blocking and collision probabilities are ob- tained, often with the use of a discrete-time Markov chain and then the performance of the backoff mechanism is studied. Here, we propose a model which allows us to study not only the throughput of nodes using IEEE 802.11 standard, but also predicts the queue distributions at each node of the studied network, as well as waiting times distributions – hence the-end-to-end delays – and the loss probabilities due to the buffer overflows. The model is based on the diffusion approximation which is a classical modelling method developed in 70-ties [12–14] to study the performance of wired networks. The model is a typical queueing network one, where service stations represent nodes, service times represent the time needed to send a packet and queues at stations model the queues of packets at nodes. Once we obtain the queue dis- tribution, we may also predict the waiting time distribution and the probability that the queue reaches its maximum value which approximates packet loss probability due to a saturated buffer. The method can be used to model networks composed of a large number of nodes, e.g. mesh networks. It also allows the analysis of transient states occurring because of time-dependent traffic inten- sity or because of the changes in the network topology. The main contribution of the article is a discussion how the CSMA/CA scheme with exponential backoff mechanism can be incorporated in this model and showing how the new model can be solved numerically. The article is organised as follows. Section 2 recalls the princi- ples of standard diffusion approximation model applied to a single station with limited queues with general independent distribu- tions of interarrival and service times, i.e. the G/G/1/N queue. Both steady state and transient state solutions are given. The transient state model was proposed previously by the authors, [6,7]. Section 3 presents the diffusion approximation model of a single node using CSMA/CA scheme with exponential backoff mechanism. Section 4 shows how the entire network of nodes with arbitrary topology can be solved. Some numerical examples are given. 0140-3664/$ - see front matter Ó 2010 Published by Elsevier B.V. doi:10.1016/j.comcom.2010.07.006 * Corresponding author. Tel.: +48 322317319x100; fax: +48 322317026. E-mail addresses: tadek@iitis.pl (T. Czachórski), kgrochla@iitis.pl (K. Grochla), Tomasz.Nycz@polsl.pl (T. Nycz), pekergin@lipn.univ-paris13.fr (F. Pekergin). Computer Communications 33 (2010) S86–S92 Contents lists available at ScienceDirect Computer Communications journal homepage: www.elsevier.com/locate/comcom