A collision resolution algorithm for a finite user model

Abstract

Kanpur 208 016 ,INDIA 1.INTRODUCTION The problem of efficient sharing of a communication channel in a time -slotted random access environment has beenconsidered by many authors [la. In such an environment there are large num er of bursty users trying t o transmit messages to a common receiver. When two or more users try t o send their messages simultaneously they collide. The problem here is of rescheduling the collided messages SO that they are eventually transmitted su ccessfu II y. Ra n d om access algorithms are essentially such scheduling algorithms. The performance objective in all such algorithms is t o achieve high through ut and small delay while maintainin stability p2].These algorithms comprise of [l) a channel access algorithm and (2) a collision resolution algorithm. Models with both finite and a potentially infinite number of users have been considered in the literature [la].In this paper we concentrate on the finite population model. For such a situation we consider the channel access t o be blocked access type i.e. no new packets are transmitted during a collision resolution epoch. The motivation for this paper is t o determine an optimal collision resolution algorithm for such a model. To facilitate our investigations we start our analysis by considerin that initial users at the beginning of the collision resolution epoch is known and obtain an optimal collision resolution algorithm. We then relax this assumption and assume that the probability distribution over the initial states (defmed in section 2.)is given. For this case we suggest a sub-optimal a1 orithm and compare algorithm. Our principal contribution in this collision multiplicity or the num % er of active its performance with t a a t of the optimal 8 1992 IEEE npaper is the dynamic programming solution for the collision resolution problem formulated as an optimal first passage problem of a Markovian Decision Process. Specifically we derive here an algorithm which is optimal in the sense of minimising the expected time of termination or collision resolution epoch when we know the number of active users and suggest a sub-optimal algorithm when we do not know this number exactly.We begin by discussing the system model in detail in section 2. We define the state of the system and its evolution with respect t o the control action. In section 3 we describe the optimal collision resolution algorithm. We illustrate this with an example. In section 4 we give a sub-optimal algorithm and present some simulation results. Section 5 concludes this paper. SYSTEM MODEL (a) Basic AssumptionsWe consider that there are N users in the system and the channel to be time slotted. The users a n transmit their packets only at the beginning of a slot. The length of the slot equals the time required for transmission of each fixed length packet. At the beginning out of these N users, say, n users are active. i.e. they have packets waiting in their buffers. We also assume that the number of active users is known to each user. As for example, the common receiver may...