Abstract
This paper studies the single server repairable queueing system with variable service rate and failure rate. The rule of variation of the service rate is that the service rate changes when the number of customers in the system reaches a certain value. The server may fail at any time, and the failure rates of idle periods and busy periods are different. The system has one reliable repairman to repair the failure server. The steady-state joint distribution of the customers number and server states is obtained by the matrix geometric solution method, the steady-state availability of the server and significant queue performances measures are evaluated. Two special cases are analyzed, and some numerical experiments are given for the illustrations of the parameters effect.
Highlights
Repairable queuing model is an important model of queuing theory research, it can be applied to a variety of real situations, such as computer networks, telecommunications, aircraft maintenance, high-speed railway maintenance, and many others
The latest studies usually assume that the system parameters such as the service rate, repair rate and failure rate are invariable, but the fact of the system parameters are variable or adjustable is an actual universal phenomenon in many service systems, even multiple parameters are variable or adjustable simultaneously in one system
Gao et al [9] analyzed a retrial queue with two-type breakdowns and delayed repairs, one type of the breakdowns cannot be repaired immediately
Summary
Repairable queuing model is an important model of queuing theory research, it can be applied to a variety of real situations, such as computer networks, telecommunications, aircraft maintenance, high-speed railway maintenance, and many others. Zhu: Single Server Repairable Queueing System With Variable Service Rate and Failure Rate fact is that the service systems are more prone to failure due to various external factors like overloading, unexpected disturbances and environmental changes when they are in working condition, while the system is relatively stable during the idle period. We introduce a new repairable queue model with variable service rate and failure rate, in which the service rate and failure rate depend on the working condition. Such models reflect the features of many actual systems.
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