MMAP/(PH,PH)/1 Queue with Priority Loss through Feedback

Divya Velayudhan Nair, Achyutha Krishnamoorthy, Agassi Melikov and Sevinj Aliyeva
Additional contact information
Divya Velayudhan Nair: Department of Mathematics, NSS College, Cherthala 688556, India
Achyutha Krishnamoorthy: Centre for Research in Mathematics, CMS College, Kottayam 686001, India
Agassi Melikov: Institute of Control Systems, National Academy of Science, Baku AZ 1148, Azerbaijan
Sevinj Aliyeva: Applied Mathematics and Cybernetics, Baku State University, Baku AZ 1148, Azerbaijan

Mathematics, 2021, vol. 9, issue 15, 1-26

Abstract: In this paper, we consider two single server queueing systems to which customers of two distinct priorities ( P 1 and P 2 ) arrive according to a Marked Markovian arrival process (MMAP). They are served according to two distinct phase type distributions. The probability of a P 1 customer to feedback is ? on completion of his service. The feedback ( P 1 ) customers, as well as P 2 customers, join the low priority queue. Low priority ( P 2 ) customers are taken for service from the head of the line whenever the P 1 queue is found to be empty at the service completion epoch. We assume a finite waiting space for P 1 customers and infinite waiting space for P 2 customers. Two models are discussed in this paper. In model I, we assume that the service of P 2 customers is according to a non-preemptive service discipline and in model II, the P 2 customers service follow a preemptive policy. No feedback is permitted to customers in the P 2 line. In the steady state these two models are compared through numerical experiments which reveal their respective performance characteristics.

Keywords: queueing system; Marked Markovian arrival process; priority loss; feedback; non-pre-emptive; preemptive (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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