Queueing models with optional cooperative services

• Published in: European journal of operational research 2016-02, Vol.248 (3), p.997-1008
• Main Author: Chakravarthy, Srinivas R.
• Format: Article
• Language: English
• Subjects: Cooperative services; Cooperatives; Customer services; Matrix-analytic method; Queueing; Queuing theory; Simulation; Studies
• ISSN: 0377-2217; 1872-6860
• DOI: 10.1016/j.ejor.2015.08.015

•Introduce cooperative services from the customers’ points of view.•Discuss effectiveness through two key performance measures.•One such performance measure is less-known and difficult to compute but useful.•Introduction of key parameters to generalize some well-known classical queues. In this paper we consider a single-server queueing model in which the customers arrive according to a versatile point process that includes correlated arrivals. An arriving customer can either request for an individual service or for a cooperative service (to be offered along with other customers with similar requests) with some pre-specified probabilities. There is a limit placed on the number of customers requiring cooperative services at any given time. Assuming the service times to be exponentially distributed with possibly different parameters depending on individual or cooperative services, we analyze this model using matrix-analytic method. Second, we simulate this model to obtain a couple of key performance measures which are difficult to compute analytically as well as numerically to show the benefit of cooperative services in queueing. Interesting numerical examples from both analytical and simulated models are discussed. We believe this type of queueing model, which is very much applicable in service areas, has not been studied in the literature.