This paper considers an M/G/1 retrial G-queue with general retrial times, in which the server is subject to working breakdowns and repairs. If the system is not empty during a normal service period, the arrival of a negative customer can cause the server breakdown, and the failed server still works at a lower service rate rather than stopping the service completely. Applying the embedded Markov...

The paper studies a closed queueing network containing a server station and k identical client stations. The client stations are subject to breakdowns, and a lifetime of each client station is assumed to be a random variable independent of all other ones having the probability distribution ) (x G . The server station is an infinite server queueing system, and client stations are single server q...

The paper deals with modelling of a finite single-server queueing system with a server subject to breakdowns. Customers interarrival times and customers service times follow the Erlang distribution defined by the shape parameter k=2 and the scale parameter 2λ or 2μ respectively. The paper demonstrates two modifications of the queueing system. In both cases we consider that server failures can o...

An M/G/1 retrial queue with two-phase service and feedback is studied in this paper, where the server is subject to starting failures and breakdowns during service. Primary customers get in the system according to a Poisson process, and they will receive service immediately if the server is available upon arrival. Otherwise, they will enter a retrial orbit and are queued in the orbit in accorda...

We consider a machine repair problem with server breakdowns, in which an unreliable server (repairman) operates the threshold recovery policy. When there are no failed machines in the system, the server leaves for a vacation. If the server returns from a vacation to find no failed machines in the system, he/she immediately takes another vacation. And the server continues in this manner until he...

This paper deals the transient analysis of a queueing system with working vacation in which server may encounter breakdowns. Customers enter batches according to Poisson process and receive service FCFS mode. Whenever finds nobody, starts during renders at slower rate than normal one. Further, we considered two types customer’s impatience balking reneging. We solved differential equations find ...

In this paper single server homogeneous finite-source retrial queueing systems are investigated. The server is assumed to be subject to random breakdowns depending on whether it is busy or idle. The failure of the server may block or unblock the system’s operations and the service of the interrupted request may be resumed or the call can be transmitted to the orbit. All random variables involve...

We present a single server in which customers arrive in batches and the server provides service one by one. The server provides two heterogeneous service stages such that service time of both stages is different and mandatory to all arriving customers in such a way that, after the completion of first stage, the second stage should also be provided to the customers. The server may subject to ran...

In this paper, we consider a BMAP/G/1 retrial queue with a server subject to breakdowns and repairs, where the life time of the server is exponential and the repair time is general. We use the supplementary variable method, which combines with the matrix-analytic method and the censoring technique, to study the system. We apply the RG-factorization of a level-dependent continuous-time Markov ch...