Queueing System with Potential for Recruiting Secondary Servers

Abstract

In this paper, we consider a single server queueing system in which the arrivals occur according to a Markovian arrival process (MAP). The served customers may be recruited (or opted from those customers’ point of view) to act as secondary servers to provide services to the waiting customers. Such customers who are recruited to be servers are referred to as secondary servers. The service times of the main as well as that of the secondary servers are assumed to be exponentially distributed possibly with different parameters. Assuming that at most there can only be one secondary server at any given time and that the secondary server will leave after serving its assigned group of customers, the model is studied as a QBD-type queue. However, one can also study this model as a GI/M/1-type queue. The model is analyzed in steady state, and a few illustrative numerical examples are presented.

Keywords

• <i>MAP</i>
• <i>QBD</i> process
• <i>GI</i>/<i>M</i>/1-queue
• computational probability