Title: A new type of negative customers

Authors: Hasnaa El Mandili; Benayad Nsiri

Addresses: GITIL Laboratory, University Hassan II, Faculty of Sciences Ain Chock Casablanca, Km 8 Eljadidaroad, P.B 5366, Maarif 20100, Morocco ' GITIL Laboratory, University Hassan II, Faculty of Sciences Ain Chock Casablanca, Km 8 Eljadidaroad, P.B 5366, Maarif 20100, Morocco

Abstract: The possibility of removing a customer before being served is one that is often absent in the theory of waiting queues. This reminds us of the concept of negative customer, which was set forth by three leading scientists: Gelenbe, Boucherie-van Dijk and Henderson. Negative customers are likely to eliminate positive ones and make them disappear. They cannot build up in the queue, and are simply lost if they arrive to an empty queue (Gelenbe, 1991; Gelenbe et al., 1991). In other contributions (Boucherie and van Dijk, 1994), we find a type of negative customers that can build up in the queue, as opposed to Gelenbe negative customers. We introduce a new type of negative client, having the same properties mentioned above, but characterised by the fact that they may remove one or more regular clients, and leave the system after being server as a regular customer. We study the existence of stationary distribution, the intensity of transition, along with the quasi-reversibility of this new type of negative customer.

Keywords: queues; quasi-reversibility; stationary distribution; negative clients; transition intensity.

DOI: 10.1504/IJCSM.2017.083751

International Journal of Computing Science and Mathematics, 2017 Vol.8 No.2, pp.193 - 200

Received: 26 Oct 2015
Accepted: 24 Sep 2016
Published online: 21 Apr 2017 *

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