Performance analysis of polling systems with retrials and glue periods

Murtuza Ali Abidini (), Onno Boxma (), Bara Kim (), Jeongsim Kim () and Jacques Resing ()
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Murtuza Ali Abidini: Eindhoven University of Technology
Onno Boxma: Eindhoven University of Technology
Bara Kim: Korea University
Jeongsim Kim: Chungbuk National University
Jacques Resing: Eindhoven University of Technology

Queueing Systems: Theory and Applications, 2017, vol. 87, issue 3, No 5, 293-324

Abstract: Abstract We consider gated polling systems with two special features: (i) retrials and (ii) glue or reservation periods. When a type-i customer arrives, or retries, during a glue period of the station i, it will be served in the following service period of that station. Customers arriving at station i in any other period join the orbit of that station and will retry after an exponentially distributed time. Such polling systems can be used to study the performance of certain switches in optical communication systems. When the glue periods are exponentially distributed, we obtain equations for the joint generating functions of the number of customers in each station. We also present an algorithm to obtain the moments of the number of customers in each station. When the glue periods are generally distributed, we consider the distribution of the total workload in the system, using it to derive a pseudo-conservation law which in turn is used to obtain accurate approximations of the individual mean waiting times. We also investigate the problem of choosing the lengths of the glue periods, under a constraint on the total glue period per cycle, so as to minimize a weighted sum of the mean waiting times.

Keywords: Polling system; Retrials; Glue periods; 60K25 (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s11134-017-9545-y

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