In this paper, we analyze a bulk input Geom/Geom/1 queue with single working vacation. Using the matrix analysis method, highly complicated PGF of the stationary queue size is firstly derived, from which we got the stochastic decomposition result for the PGF of the stationary queue size. It is important that we find the biparameter addition theorems of the conditional negative binomial distribu...

Switches in interconnection networks for highly parallel shared memory computer systems may be implemented with different internal buffer structures. For a 2×2 synchronous switch, previous studies have often assumed a switch composed of two queues, one at each output, each of which has unbounded size and may accept two inputs every clock cycle. Hardware implementations may actually use simpler ...

We consider single-server queues with exponentially distributed service times, in which the arrival process is governed by a semi-Markov process (SMP). Two service disciplines, processor sharing (PS) and random service (RS), are investigated. We note that the sojourn time distribution of a type-l customer who, upon his arrival, meets k customers already present in the SMP/M/1/PS queue is identi...

in this paper, we study the network location problem for two congestible facilities, considering impatient customers. we suppose that when a customer arrives his/her corresponding facility and faces a queue with the size more than a predetermined threshold, the customer decides not to join the queue but to go to the closest facility to current facility. in the second facility, if the queue size...

This paper deals with machine repair problem with balking and reneging. There is provision of mixed standby (warm and cold) components to replace the failed machines. The lifetime and repair time are assumed to have exponential distribution. Birth-death technique is suggested to obtain the queue size distribution in explicit form. A repair facility of C permanent repairmen is facilitated to rep...

We consider the dispatching problem in a sizeand state-aware multi-queue system with Poisson arrivals and queue-specific job sizes. By sizeand state-awareness, we mean that the dispatcher knows the size of an arriving job and the remaining service times of the jobs in each queue. By queue-specific job sizes, we mean that the time to process a job may depend on the chosen server. We focus on min...

Queues with Markovian arrival and service processes, i.e., MAP/MAP/1 queues, have been useful in the analysis of computer and communication systems and di erent representations for their stationary sojourn time and queue length distribution have been derived. More speci cally, the class of MAP/MAP/1 queues lies at the intersection of the class of QBD queues and the class of semi-Markovian queue...

We consider a model of two M/M/1 queues, served by a single server. The service policy for this polling model is of threshold type: the server serves queue 1 exhaustively, and does not remain at an empty queue if the other one is non-empty. It switches from queue 2 to queue 1 when the size of the latter queue reaches some level T , either preemptively or non-preemptively. All switches are insta...

We consider a bulk service G I / M / l queue with service rates depending on service batch size. If there are n customers waiting at the completion of service, min(n, I\) customers enter service. We show that the queue size and the service batch size at points of arrivals form an embedded Markov chain and the steady-state probabilities of this Markov chain have the matrix geometric form. We des...