Randomized controlling arrival for a queueing system with subject to server breakdowns

Abstract

This paper considers the optimal management problem of a finite-capacity M/M/1/K queueing system with -policy in which the server may break down while working. When the number of customers reaches its capacity K, no further arriving customers are allowed to enter the system. Customers are allowed to system with probability p or the customers are still unable to enter the system with probability 1 − p as the queue length decreases to a certain threshold value F. By applying the birth-and-death process, some important performance measures are derived. A cost model, developed to determine the optimal continuous and discrete control parameters for the -policy at a minimum cost, and sensitivity analysis are also studied.

Keywords:

• breakdowns
• cost
• control
• ⟨p,F⟩-policy
• server start-up

AMS Subject Classifications:

• 60K25
• 90B22
• 65K05
• 90C53
• 68M20