We propose a linear model of the throughput of the IEEE 802.11 Distributed Coordination Function (DCF) protocol at the data link layer in non-saturated traffic conditions. We show that the throughput is a linear function of the packet arrival rate (PAR) $\lambda$ with a slope depending on both the number of contending stations and the average payload length. We also derive the interval of validity of the proposed model by showing the presence of a critical $\lambda$, above which the station begins operating in saturated traffic conditions. The analysis is based on the multi-dimensional Markovian state transition model proposed by Liaw \textit{et al.} with the aim of describing the behaviour of the MAC layer in unsaturated traffic conditions. Simulation results closely match the theoretical derivations, confirming the effectiveness of the proposed linear model.
Modelling of the DCF at the MAC layer of the series of IEEE 802.11 standards has recently garnered interest in the scientific community [1]- [6]. After the seminal work by Bianchi [1] who proposed a bi-dimensional Markov model of the back-off stage procedure adopted by the DCF in saturated conditions, many papers have focused on various facets of basic access mechanism providing extensions to most recent versions of the IEEE 802.11 series of standards [7]. Recently, in [3] the authors proposed a novel fixed-point analysis of the DCF providing an effective framework for analyzing single cell IEEE 802.11 WLANs without resorting to the bidimensional contention model [1].
Practical networks usually operate in non-saturated conditions and data traffic is mainly bursty. Under these operating conditions, Bianchi’s model does not describe accurately the behaviour of the throughput at the MAC layer. In this respect, in [4]- [5] the authors proposed two different bi-dimensional Markov models accounting for unsaturated traffic conditions, extending the basic bi-dimensional model proposed in [1].
In this paper we take a different approach with respect to works [4]- [5]. Upon starting from the bi-dimensional model proposed by Liaw et al. in [4], we show that the behaviour of the throughput of the IEEE 802.11 DCF in unsaturated conditions can be described by a linear relation that, with respect to the PAR λ, depends on two network parameters: the number N of contending stations, and the average size E[P L] of the transmitted packets. This is one of the key F. Daneshgaran is with ECE Dept., CSU, Los Angeles, USA. M. Laddomada, F. Mesiti, and M. Mondin are with DELEN, Politecnico di Torino, Italy. contribution of the paper: no simulations are needed for throughput evaluation since it can be theoretically predicted employing the model S(λ) = N • E[P L]λ developed in Section III. Of course, the limit of validity of such a model has to be clearly identified, and it represents another contribution of this paper. To this end, we derive the interval of validity of the proposed model with respect to the PARs at the MAC layer. We demonstrate the existence of a critical PAR, λ c , which discriminates the unsaturated region, characterized by the range λ ∈ [0, λ c ), from the saturation zone identified by any λ ∈ [λ c , +∞).
For conciseness, we invite the interested reader to refer to [4] for many details on the considered bi-dimensional Markov model, and references therein to get a picture of the topic addressed in this letter. Briefly, Liaw et al. extended the saturated Bianchi’s model by introducing a new idle state, not present in the original Bianchi’s model, accounting for the case in which the station buffer is empty, after a successful completion of a packet transmission. The main advantages of such a model rely on its simplicity and the effectiveness in describing the dynamics of the DCF in unsaturated traffic conditions, while basic hypotheses are the same as in Bianchi’s model.
Paper outline is as follows. In section II, we briefly recall the main probabilities needed for developing the proposed linear model, evaluate the throughput and present the adopted traffic model. Finally, Section III presents the linear model of the throughput along with simulation results.
The bi-dimensional contention Markov model proposed in [4] governs the behaviour of each contending station through a series of states indexed by the pair
, whereby i identifies the backoff stage, and k ∈ [0, W i -1] the backoff counter. The other parameters needed in the proposed framework can be summarized as follows: τ is the probability that a station starts a transmission in a randomly chosen slot time (ST), q is the probability that there is at least a packet in the queue after a successful transmission,
is the size of the ith contention window, W 0 is the minimum size of the contention window, P I,0 is the probability of having at least one packet to be transmitted in the queue when the system is in idle state, and p is the collision probability defined as in [1]
Stationary probability b I of being in the idle state is:
whereby b 0,0 is defined as follows:
By employing the normalization condition [1], it is possible to obtain:
Next line of pursuit is the computation of the system throughput. Putting together Eq.s (1), ( 4), a nonlinear system can be defined and solved numerically, obtaining the values of τ and p. The solution of the previous system is used for evaluating the throughput, defined as the ratio between the average payload information transmitted in a ST and the average length, T av , of a ST:
whereby E[P L] is the average packet payload length (expressed in bits), P t is the probability that there is at least one transmission in the considered ST, with N stations contending for the channel, each transmitting with probability τ , i.e., P t = 1 -(1 -τ ) N . Probability P s is the conditional probability that a packet transmission oc
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