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.
Highlights
This paper investigates optimization analysis of the N-policy M/G/1 queue with working breakdowns
Based on the matrix analytic method, Liou [4] found the steady-state probabilities of the number of customers in the M/M/1 queue with working breakdowns and impatient customers
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]
Summary
This paper investigates optimization analysis of the N-policy M/G/1 queue with working breakdowns. Symmetry 2020, 12, 583 of maximum entropy to investigate the N-policy M/G/1 queue with server breakdowns and general startup times. 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. 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.
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