Tandem queues with subexponential service times and finite buffers

Abstract

We focus on tandem queues with subexponential service time distributions. We assume that number of customers in front of the first station is infinite and there is infinite room for finished customers after the last station but the size of the buffer between two consecutive stations is finite. Using (max,+) linear recursions, we investigate the tail asymptotics of transient response times and waiting times under both communication blocking and manufacturing blocking schemes. We also discuss under which conditions these results can be generalized to the tail asymptotics of stationary response times and waiting times. Finally, we provide numerical examples to investigate the convergence of the tail probabilities of transient response times and waiting times to their asymptotic counter parts.

Applications of queues in hospitals in Istanbul

“…If the queue that the costumer will go is full, then the server will wait for opening the place. (Kim & Ayhan, 2010) In the blocking case, patients may not get service and leave the system if there is no place in beds. In this case, patients may search for another hospital or less costly services.…”