Optimal Management of a Removable and Non-Reliable Server in an Infinite and a Finite M/H_k/1 Queueing System

Abstract

We consider a single removable and non-reliable server in both infinite capacity and finite capacity queueing systems with Poisson arrivals and k-type hyper-exponential distribution for the service times operating under the N policy. The server may be turned on at arrival epochs or off at departure epochs. Breakdown and repair times of the server are assumed to follow a negative exponential distribution. Cost model for infinite capacity queueing system (say cost model 1) is developed to determine the optimal operating policy. Cost model for finite capacity queueing system (say cost model 2) is developed to determine the optimal operating policy and the optimal system capacity, simultaneously. This paper presents the optimal operating policy, the optimal system capacity, the minimum expected cost based on specific values given to the system parameters, as well as to the cost elements. The sensitivity analysis is also investigated.

On M/G/1 system under NT policies with breakdowns, startup and closedown

“…Later, Wang and Ke [15] investigated three control policies in an M/G/1 queueing system and proved that in three control policies, the probability that the server is busy in the steady-state is equal to the traffic intensity. Recently, Wang et al [16] extended Wang and YenÕs system [11] to unreliable server case.…”

A Nonlinear Programming Approach for a Fuzzy Queue with an Unreliable Server

“…The system can handle only one job at a time-and the system resumes as soon as the interruption ends. The arrival rate, service rate, breakdown rate and repair rate are fuzzy numbers represented by [10,20,30,40] The manager of the system wants to know the system characteristic such as how many hours the processing system is idle. By continuing in a similar manner explained in Example 1, we have fig.…”

“…His system was extended to the GI/G/I case by Sengupta [8]. Li et al [6] and Wang [10] investigated the behaviour of the unreliable server, and the effect the server breakdowns and repairs in the M/G/I queuing models and he investigated the controllable M/H K /I queuing systems with an unreliable server recently.…”

The Analysis of Performance Measures of Generalized Trapezoidal Fuzzy Queuing Model with an Unreliable Server

“…The first ordinary M/G/I queuing system which has interrupted services and priorities was first proposed by Gaver [1]. Then Sengupta [2] extended the system proposed by Gaver [1] to the GI/G/I case. The behavior of the of the unreliable server and the impact of the unreliable server on the server breakdowns and repairs of the M/G/I queuing models was first established by the Li [3] and Wang [4].…”