Performance analysis of markov modulated IEEE 802.15.4 beacon-enable mode

Abstract

In this paper, we study the throughput stability, mean queueing delay and energy consumption issues of IEEE 802.15.4 MAC protocol. We model the network as a multi-queue single-server system and derive the service time distribution of head-of-line packets from a Markov Chain of beacon-enable mode in an unsaturated traffic environment. Two transmission schemes of uplink traffic, the non-acknowledged transmission and acknowledged transmission, are studied with probabilistic exponential backoff scheduling algorithm. We obtain the characteristic equation of network throughput and power consumptions of each node in closed form, from which the stable throughput region and bounded mean delay region are specified with respect to the retransmission factor. Furthermore, we also show that the energy consumption of each node can be kept small within the stable throughput region. All analytical results presented in this paper are verified by simulations.

Appendix 1: Service time distribution for IEEE 802.15.4

Since the service of each HOL packet starts from state $CCA_{0}^{1}$, therefore the first and second moments of service time, E[X] and E[X ²], can be derived from the generating function $CCA_{0}^{1} (z).$ We take the first and second derivatives of (12), and then can solve the set of simultaneous equations for the first and second moments of the service time of HOL packets with exponential backoff scheme as follows:

$$ E[X] = CCA_{0}^{1\prime } (1) = \frac{aq}{{pq_{0} \left( {\alpha_{1} \alpha_{2} + q - 1} \right)}} + \frac{a}{{\alpha_{2} p}} + \frac{aM}{p}, $$

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$$ E[X^{2} ] = CCA_{0}^{1\prime } (1) + CCA_{0}^{1\prime } (1) = B\left( {p,q} \right) + C\left( {p,q} \right)\mathop {\lim }\limits_{K \to \infty } \left( {\frac{{1 - \alpha_{1} \alpha_{2} }}{{q^{2} }}} \right)^{K} . $$

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where

$$ \begin{aligned} B(p,q) & = a^{2} \{ \frac{{2\left( {1 - 2\alpha_{2} } \right)\left( {1 - p} \right)q + 2q}}{{p^{2} q_{0} \alpha_{2} \left( {\alpha_{1} \alpha_{2} + q - 1} \right)}} + \frac{{2q^{2} \left( {1 - p} \right)}}{{p^{2} q_{0}^{2} \left( {\alpha_{1} \alpha_{2} + q - 1} \right)^{2} }} + \frac{{2q\left( {1 + \alpha_{1} - 2\alpha_{1} \alpha_{2} } \right) - 2q^{2} }}{{pq_{0} \left( {\alpha_{1} \alpha_{2} + q - 1} \right)^{2} }}, \\ & \quad + \frac{{2q^{3} }}{{pq_{0}^{2} \left( {\alpha_{1} \alpha_{2} + q - 1} \right)\left( {\alpha_{1} \alpha_{2} + q^{2} - 1} \right)}} + \frac{{2 + 4M\alpha_{2} \left( {1 - \alpha_{2} } \right) - 2\alpha_{2} p\left( {M + \alpha_{2} + 1} \right)}}{{\alpha_{2}^{2} p^{2} }} \\ & \quad + \frac{{2\left( {M + 2} \right)\left( {1 - p} \right)q + 2Mq}}{{p^{2} q_{0} \left( {\alpha_{1} \alpha_{2} + q - 1} \right)}} + \frac{{\left( {M + 2} \right)\left( {2M - Mp + p} \right)}}{{p^{2} }}\} + E[X] \\ \end{aligned} $$

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and

$$ C(p,q) = \frac{{2\left( {\alpha_{1} \alpha_{2} + q^{2} - 1} \right)\left( {\alpha_{1}^{2} \alpha_{2}^{2} q - \alpha_{1} \alpha_{2} q + \alpha_{1} \alpha_{2} + q - 1} \right) - 2q^{3} \alpha_{1}^{2} \alpha_{2}^{2} }}{{pq_{0}^{2} \alpha_{1}^{2} \alpha_{2}^{2} \left( {\alpha_{1} \alpha_{2} + q - 1} \right)\left( {\alpha_{1} \alpha_{2} + q^{2} - 1} \right)}}. $$

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