Abstract
In this paper, we consider two single server queueing systems to which customers of two distinct priorities (P1 and P2) arrive according to a Marked Markovian arrival process (MMAP). They are served according to two distinct phase type distributions. The probability of a P1 customer to feedback is θ on completion of his service. The feedback (P1) customers, as well as P2 customers, join the low priority queue. Low priority (P2) customers are taken for service from the head of the line whenever the P1 queue is found to be empty at the service completion epoch. We assume a finite waiting space for P1 customers and infinite waiting space for P2 customers. Two models are discussed in this paper. In model I, we assume that the service of P2 customers is according to a non-preemptive service discipline and in model II, the P2 customers service follow a preemptive policy. No feedback is permitted to customers in the P2 line. In the steady state these two models are compared through numerical experiments which reveal their respective performance characteristics.
Highlights
In this paper, we discuss two queueing models arising due to feedback of customers from a high priority queue (P1 queue) joining a lower priority queue (P2 queue), in a single server queueing system
The probability for feedback at a service completion epoch is θ which is independent of the feedback by other customers and the number of customers in the system
Because the customers who feedback join a new queue, our model provides the best way to identify such customers, provided low priority customers are not admitted to the system
Summary
We discuss two queueing models arising due to feedback of customers from a high priority queue (P1 queue) joining a lower priority queue (P2 queue), in a single server queueing system. The probability for feedback at a service completion epoch is θ which is independent of the feedback by other customers and the number of customers in the system They are to join a low-priority P2 queue. This paper is a further extension of [1] Prior to introducing this type of feedback of customers, only two types of feedback were considered in the literature: (i) feedback to the tail end of the queue and (ii) continue service as a feedback customer on completion of the first service. The problems discussed in this paper have several practical utilities This has certain advantages, which include minimizing unnecessarily bothering the server with questions that were clarified in the earlier rounds of service. In this paper MMAP arrival of customers and distinct phase-type distributed service time for the two types of customers, are considered. Before going to further details of the paper, we provide literature review on the two topics—feedback and priority queue
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
