Optimization Analysis of the N Policy M/G/1 Queue with Working Breakdowns

Abstract

This paper deals with the N policy M/G/1 queue with working breakdowns. The supplementary variable and probability generating function techniques are implemented to develop the steady-state results. The stability condition of a stable queue, as well as several system performance measures, are also derived. A two-stage optimization method is employed to determine the optimal threshold N and the optimal joint values of two mean service rates until the stability constraint is satisfied. To demonstrate the effectiveness of two-stage optimization method, some numerical results are presented. Finally, we carry out sensitivity analysis for the expected cost function with numerical illustrations.Symmetry 2020, 12, 583 2 of 16 of maximum entropy to investigate the N-policy M/G/1 queue with server breakdowns and general startup times. Using the same approach, Ke and Lin [10] approximated the steady-state probability distributions of the queue length for the N-policy M [x] /G/1 queue with an unreliable server and a single vacation. The optimal control of the N-policy M/G/1 queueing system with server breakdowns and general startup times was examined by Wang et al. [11]. They applied the direct search method to determine the optimal threshold N at the minimum cost. Jain and Bhargava [12] performed cost analysis of the N-policy for the machine repair problem with mixed standbys and an unreliable server. An N-policy M X /M/1 queueing system with server startup and breakdowns was analyzed by Vemuri et al. [13], where service was in two phases. Singh et al. [14] focused on the investigation of the N-policy queue with an unreliable server, state-dependent arrival rates, two phases of service, and m phases of repair. Moreover, Yang and Ke [15] applied the supplementary variable technique to analyze the (p, N)-policy M/G/1 queue with an unreliable server and a single vacation. Chen and Wang [16] address the sensitivity analyses of a retrial machine repair problem with warm standby units and a single server under the N-policy.Over the years, there has been extensive literature on N-policy queues with server breakdowns, in which the server stops working completely during the breakdown period. However, there are no studies investigating the N-policy queue with working breakdowns. This queueing model accommodates many real-world systems, such as computer systems, assembly systems, and manufacturing systems. Thus, it motivates us to focus on the analysis of the N-policy M/G/1 queue with working breakdowns. The purpose of this paper is three-fold.

The k-out-of-n:G System Viewed as a Multi-Server Queue

“…Thus, various extensions are possible. N-policy queuing systems with server breakdowns (both working and non-working breakdowns) are studied extensively in the queuing literature (for example, [5][6][7]).…”

Entropy Analysis of a Flexible Markovian Queue with Server Breakdowns

“…The earliest document using entropy maximization in the context of queues that came to our attention is that of Bechtold et al [ 3 ]. Among the latest theoretical papers applying the maximum entropy principle we cite Yen et al [ 4 ], Shah [ 5 ], and Singh et al [ 6 ], while She et al [ 7 ], Giri and Roy [ 8 ], and Lin et al [ 9 ] present recent applications.…”

Analysis of a Finite Markovian Queue With Server Breakdown, Setup Time and State Dependent Rate Under N-Policy Strategy

“…Kumar and Jain [8] proposed threshold 'N' based policy for the performance prediction of (M, m) degraded machine repair problem with spare provisioning by including the concepts of the multi-heterogeneous servers, standby switching failure and multiple vacations. In recent years, Jiang et al [6], Lan and Tang [9], Bu et al [1] and Yen et al [14] developed some queueing models for congestion problems under N-policy strategy. Sethi et al.…”