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ZOR -Methods and Models of Operations Research (1993) 38: 55-76 Cyclic Bernoulli Polling I

Summary: ZOR - Methods and Models of Operations Research (1993) 38: 55-76
Cyclic Bernoulli Polling I
INRIA Centre Sophia Antipolis, 06565 Valbonne Cedex, France
Department of Statistics, Tel-Aviv University, Tel-Aviv 69978, Israel
Abstract: We introduce, analyse and optimize the class of Bernoulli random polling systems. The
server moves cyclically among N channels (queues), but Change-over times between stations are
composed of walking times required to 'move' from one channel to another and switch-in times that
are incurred only when the server actually enters a station to render service. The server uses a
Bernoullirandom mechanism to decide whether to serve a queue or not: upon arrival to channel i,
it switches in with probability Pi, or moves on to the next queue (w.p. 1 - pl) without serving any cus-
tomer (e.g. packet or job). The Cyclic Bernoulli Polling (CBP) scheme is independent of the service
regime in any particular station, and may be applied to any service discipline. In this paper we
analyse three different service disciplines under the CBP scheme: Gated, Partially Exhaustive and
Fully Exhaustive. For each regime we derive expressions for (i) the generating functions and
moments of the number of customers (jobs) at the various queues at polling instants, (ii) the expected
number ofjobs that an arbitrary departing job leaves behind it, and (iii) the LST and expectation of
the waiting time of a cutomer at any given queue. The fact that these measures of performance can
be explicitly obtained under the CBP is an advantage over all "parameterized" cyclic polling schemes


Source: Altman, Eitan.- Projet Maestro, Université de Nice Sophia Antipolis


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