Analysis of queues in a random environment with impatient customers

A PH i /PH i

“…Eisen and Tainiter [38] first considered a queuing process with two mean arrival and service rates. Queuing models in an RE where the interarrival time and service time are subject to exponential distribution M, such as M/M/1, M/M/C, and M/M/∞ queuing models were later explored by Yechiali and Naor [27]; Neuts [39]; O'cinneide and Purdue [40]; Krenzler and Daduna [30]; and Yu and Liu [29]. More recent works can be found in the study by Pang et al [41] and Naumov and Samouylov [42].…”

“…Given the strong hypothesis on the exponentially distributed interarrival time in the M/G (n)/C/C state-dependent queuing model, Jiang et al [52] developed a discrete event simulation model based on a G/G(n)/C/C state-dependent queuing system. Hu et al [15] established a PH/PH(n)/C/C [22] Transient M ✓ Ammar [23] Transient M ✓ Hu et al [13] Transient M ✓ ✓ Yuhaski et al [14] Stationary M ✓ Jain and Smith [24] Stationary M ✓ Smith and Cruz [25] Stationary M ✓ Hu et al [15] Stationary PH ✓ Zhu et al [26] Stationary PH ✓ Yechiali and Naor [27] Stationary M ✓ ✓ Neuts [28] Stationary M ✓ ✓ Baykal-Grsoy et al [3] Stationary M ✓ ✓ Yu and Liu [29] Stationary M ✓ ✓ Krenzler and Daduna [30] Stationary M ✓ ✓ Kim et al [20] Stationary We aim to propose a stationary PH(i)/PH(i, n)/C/C state-dependent queuing model in an RE which comprehensively considers the general randomness in arrival and service, the state-dependent service time and the effect of randomly changing environmental factors. It is very difficult to solve the proposed PH(i)/PH(i, n)/C/C state-dependent queuing model in an RE.…”

Transient analysis of impatient customers in an M/M/1 disasters queue in random environment

“…Sudhesh (2010) derived time-dependent system size probabilities for the M/M/1 queue with system disasters and customer impatience via generating functions and continued fractions. Lately, Yu and Liu (2017) studied the M/M/1, M/M/c and M=M=1 queues in a random environment with impatient customers; they focused on obtaining the explicit expressions of the performance measures in a steady-state using a technical decomposition on the coefficient of the corresponding ordinary differential equation.…”

“…Motivated by these applications and the astounding works of Paz and Yechiali (2014), Yu and Liu (2017) and Jiang et al (2015), in this paper we further develop the queueing system presented by Paz and Yechiali (2014) in which the M/M/1 queue was studied. We extend this system to an M/M/1 queue operating in a multi-phase random environment with disasters and impatience behavior.…”