Performance analysis of single server non-Markovian retrial queue with working vacation and constant retrial policy

Abstract

This paper analyses an M/G/1 retrial queue with working vacation and constant retrial policy. As soon as the system becomes empty, the server begins a working vacation. The server works with different service rates rather than completely stopping service during a vacation. We construct the mathematical model and derive the steadystate queue distribution of number of customer in the retrial group. The effects of various performance measures are derived.

An M/G/1 retrial queue with single working vacation under Bernoulli schedule

“…Using the matrix-analytic method, Tao et al [16] considered an M/M/1 retrial queue with collisions and working vacation interruption under N-policy, Upadhyaya [26] analyzed a discrete-time Geo X /Geo/1 retrial queue with working vacations. Using the method of supplementary variable, Aissani et al [1] and Jailaxmi et al [28] both generalized the model of [27] to an M/G/1 queue with constant retrial policy, and Arivudainambi et al [4] analyzed an M/G/1 queue with general retrial time policy. Gao et al [24] discussed an M/G/1 retrial queue with general retrial times and working vacation interruption, the discrete-time Geo X /G/1 queue was investigated by Gao and Wang [23].…”

An M/G/1 Retrial G-Queue with General Retrial Times and Working Breakdowns

“…Retrial queueing systems with working vacations were first studied by Do [28], and the M/M/1 model is motivated by the performance analysis of a media access control function in wireless networks. For more retrial queues with working vacations, readers can refer to Jailaxmi et al [29] and Rajadurai et al [30,31]. The concept of working breakdown introduced by Kalidass and Kasturi [11] does make sense in real life.…”

Performance of an M/M/1 Retrial Queue with Working Vacation Interruption and Classical Retrial Policy

“…Using the matrix analytic method, Do [12], Li et al [13], Liu and Song [14], and Tao et al [15] obtained the stationary probability distribution and showed the conditional stochastic decomposition for the queue length. Using the method of a supplementary variable, Aissani et al [16] and Jailaxmi et al [17] both generalized the model of [12] to an M/G/1 queue. Gao and Wang [18] analyzed a Geo /G/1 retrial queue with general retrial times and working vacation interruption, and the continuous-time M/G/1 queue was investigated by Gao et al [19].…”