Analysis of queueing systems with customer interjections
The paper deals with a single server queueing system, where two types of customers, which join a single queue of infinite capacity, arrive according to a Poisson process. The first type of customers are normal customers and join the queue at the end, whereas the second type of customers are interjecting customers which do not interrupt the service in progress and try to cut in the queue as follows. Upon arrival, the customer contacts the first customer waiting in the queue for a possible interjection. That customer (regardless of its type) may let the new customer cut in with probability \(\eta_C\), i.e., the new customer takes the first position in the queue. If the first customer refuses the interjection request, the new customer contacts the second customer in the queue. The process repeats until either the customer interjects successfully or joins the queue at the end if all customers refuse its interjection request. The service times of all customers are exponentially distributed with the same mean. For this system, denoted by M[2]/M/1/FCFS, the waiting times of normal customers and interjecting customers are studied; in particular, their mean and variance are characterized analytically and numerically. The basic queueing model is extended to an MMAP[2]/PH/1/FCFS queue, and an algorithm is developed for computing the means and variances of the waiting times of normal, interacting and arbitrary customers. The results are obtained by using matrix analytic methods. Furthermore, numerical results are presented.
scientific article; zbMATH DE number 6131913
scientific article