Comparison results for M/G/1 queues with waiting and sojourn time deadlines

• Published in: Journal of applied probability Vol. 56; no. 2; pp. 524 - 532
• Main Author: Inoue, Yoshiaki
• Format: Journal Article
• Language: English
• Published: Cambridge, UK Cambridge University Press 01-06-2019; Applied Probability Trust
• Subjects: Customer services; Customers; Deadlines; Integral equations; Markov analysis; Queues; Queuing theory; Random variables; Research Papers; impatient customer; Secondary 68M20; Primary 60K25; virtual waiting time; loss probability; M/G/1 queue; stochastic order
• ISSN: 0021-9002; 1475-6072
• DOI: 10.1017/jpr.2019.25

This paper considers two variants of M/G/1 queues with impatient customers, which are denoted by M/G/1+Gw and M/G/1+Gs. In the M/G/1+Gw queue customers have deadlines for their waiting times, and they leave the system immediately if their services do not start before the expiration of their deadlines. On the other hand, in the M/G/1+Gs queue customers have deadlines for their sojourn times, where customers in service also immediately leave the system when their deadlines expire. In this paper we derive comparison results for performance measures of these models. In particular, we show that if the service time distribution is new better than used in expectation, then the loss probability in the M/G/1+Gs queue is greater than that in the M/G/1+Gw queue.