A preemptive discrete-time priority buffer system with partial buffer sharing

Abstract

a b s t r a c tThis paper considers a Geo/Geo/1 discrete-time queue with preemptive priority. Both the arrival and service processes are Bernoulli processes. There are two kinds of customers: low-priority and high-priority customers. The high-priority customers have a preemptive priority over low-priority customers. If the total number of customers is equal or more than the threshold (k), the arrival of low-priority customers will be ignored. Hence the system buffer size is finite only for the low-priority customers. A recursive numerical procedure is developed to find the steady-state probabilities. With the aid of recursive equations, we transform the infinite steady-state departure-epoch equations set to a set of (k + 1) Â (k + 2)/2 linear equations set based on the embedded Markov Chain technique. Then, this reduced linear equations set is used to compute the steady-state departureepoch probabilities. The important performance measures of the system are calculated. Finally, the applicability of the solution procedure is shown by a numerical example and the sensitivity of the performance measures to the changes in system parameters is analyzed.

A Discrete-Time Queue with Preferred Customers and Partial Buffer Sharing

“…In the last 20 years a number of the discrete-time queueing models have been studied, details of which may be found in papers [5][6][7]. The preemptive queuing also became the focus of discussion by the papers such as [8][9][10]. Particularly in [11], a novel recursive method for Geo1/Geo2/G/1/K+1 queue with partial buffer sharing was developed.…”

“…Particularly in [11], a novel recursive method for Geo1/Geo2/G/1/K+1 queue with partial buffer sharing was developed. In 2010, Jolai et al [8] considered a preemptive discrete-time priority buffer system with partial buffer sharing. In that paper, they obtained the steady probability of the system by using the recursive method.…”

A preemptive priority queue with preemptions penalty

“…Once the service of the lower-priority customer is finished, the server starts servicing the higher-priority customer. In a preemptive priority queue (see e.g., [6,11,13,15]), on the contrary, the service of a lower-priority customer will be interrupted at once if a higherpriority customer arrives and will not be resumed until the system is again void of higher-priority customers. It is easily seen that the preemptive category is favorable to higherpriority customers, because their delays are not at all influenced by lower-priority customers.…”