Title: On the study of simultaneous service by random number of servers with retrial and preemptive priority

Authors: Resham Vinayak; S. Dharmaraja; Viswanathan Arunachalam

Addresses: Department of Mathematics, Indian Institute of Technology Delhi, Hauz Khas, New Delhi – 110016, India ' Department of Mathematics, Indian Institute of Technology Delhi, Hauz Khas, New Delhi – 110016, India ' Department of Mathematics, Universidad de los Andes, Cra 1 No 18A-10, Bogota, Colombia; Department of Statistics, Universidad Nacional de Colombia, Carrera 45 No 26-85, Bogota, Colombia

Abstract: In this paper, we propose to study the performance of a multi-server queuing system in which a customer requires simultaneous service from a random number of servers with the queuing disciplines retrial and preemptive priority. The infinitesimal generator matrix is presented for the proposed model and steady state measures are discussed. In particular, analytical expressions are obtained for the case where a customer (single type) requires simultaneous service from a random number of servers. Also, the generalised stochastic Petri net (GSPN) is developed for the proposed model and the particular cases. The performance of the models is analysed and compared, in terms of average system size and throughput. It is found that queuing systems in which a customer requires simultaneous service from a random number of servers performs better when the queuing discipline of retrial is appended into the system.

Keywords: multi-server queuing; retrial; preemptive priority; random number of servers; simultaneous service; infinitesimal generator matrix; generalised stochastic Petri nets; GSPN; modelling; average system size; throughput.

DOI: 10.1504/IJOR.2014.060516

International Journal of Operational Research, 2014 Vol.20 No.1, pp.68 - 90

Received: 07 Jul 2012
Accepted: 11 Nov 2012
Published online: 21 Jun 2014 *

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