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Paper details
Number 1 - March 2017
Volume 27 - 2017
Analysis of an MAP/PH/1 queue with flexible group service
Arianna Brugno, Ciro D’Apice, Alexander Dudin, Rosanna Manzo
Abstract
A novel customer batch service discipline for a single server queue is introduced and analyzed. Service to customers is
offered in batches of a certain size. If the number of customers in the system at the service completion moment is less
than this size, the server does not start the next service until the number of customers in the system reaches this size or a
random limitation of the idle time of the server expires, whichever occurs first. Customers arrive according to a Markovian
arrival process. An individual customer’s service time has a phase-type distribution. The service time of a batch is defined
as the maximum of the individual service times of the customers which form the batch. The dynamics of such a system
are described by a multi-dimensional Markov chain. An ergodicity condition for this Markov chain is derived, a stationary
probability distribution of the states is computed, and formulas for the main performance measures of the system are
provided. The Laplace–Stieltjes transform of the waiting time is obtained. Results are numerically illustrated.
Keywords
queueing system, batch service, multi-rate service, stationary distribution, optimization