We study a M/Ek/1 queueing model where the service is provided in two phases one by one in secession. The server operates N-policy. Customer’s arrival rate depends on the state of the server. The service mechanism breakdowns occur only during active service and repair process may not take place immediately due to non-availability of the repair facility. We derive the steady state solutions by u...

We analyze a single server queue with Poisson arrivals, two stages of heterogeneous service with different (arbitrary) service time distributions subject to random breakdowns and compulsory server vacations with general (arbitrary) vacation periods. After first-stage service the server must provide the second stage service. However, after the completion of each second stage service, the server ...

In this paper we present the tool spn2mgm that can be used to construct and solve stochastic Petri nets using matrix-geometric techniques. The tool automatically recognizes the \matrix-geometric structure" of the Markov chain underlying the stochastic Petri net, and solves the Markov chain with these well-known and ef-cient techniques. We informally characterize the class of stochastic Petri ne...

We consider an unreliable multi-server queue in which the rate of servers’ breakdowns increases when the number of broken servers grows. To prevent quick degradation of the system, it is proposed to switch to a quarantine regime when the number of broken servers exceeds some threshold and to maintain this regime until the number of broken servers becomes less than another threshold. During the ...

Abstract This paper studies a batch arrival queueing system in which the server may face occasional random breakdowns. The repair process does not start immediately after a breakdown and there is a delay time waiting for repairs to start. Further, after every service completion the server has the option to leave for a vacation with probability p or continue serving with probability1 − p. The ma...

An M/G/1 retrial queueing system with breakdowns have been studied in fuzzy environment. The arrival rate,retrial rate, service rate,failure rate and repair rate of server are all fuzzy numbers. For this model we obtain some system characteristics such as mean orbit size ,mean normal queue size and mean system size. The α cut approach is used to transform fuzzy queues with an unreliable server ...

Abstract: The present investigation deals with M/G/1 retrial queue with unreliable server and general retrial times. The server is subject to breakdowns and takes some setup time before starting the repair. The server renders first essential phase of service (FES) to all the arriving customers whereas second optional phase services (SOS) are provided after FES to only those customers who opt fo...