This paper analyzes a discrete-time finite buffer renewal input queue with multipleworking vacations where services are performed in batches of maximum size “b”. The service times bothduring a regular service period and vacation period and vacation times are geometricallydistributed. Employing the supplementary variable and imbedded Markov chain techniques, wederive the steady-state queue length distributions at pre-arrival, arbitrary and outsideobserver’s observation epochs. Based on the queue length distributions, some performancemeasures and waiting time distribution in the queue have been discussed. Finally,numerical results showing the effect of model parameters on the key performance measuresare presented.

In a multi server queuing system, buffer size is often larger than the number of servers.This necessitates queuing and waiting for some customers. Customers become impatient whilewaiting for service. Additionally, they may also become impatient if service is notoffered at the desired rate. This paper analyses a finite buffer multi server queuingsystem with the additional restriction that customers may balk as well as renege. Closedform expressions of a number of performance measures are presented. A design problem isdiscussed to demonstrate the results derived.

In many service, production, and traffic systems there are multiple types of customers requiring different types of ‘servers’, i.e. different services, products, or routes. Often, however, a proportion of the customers are flexible, i.e. they are willing to change their type in order to achieve faster service, and even if this proportion is small, it has the potential of achieving large performance gains. We generalize earlier results on the optimality of ‘join the shortest queue’ (JSQ) for flexible arrivals to the following: arbitrary arrivals where only a subset are flexible, multiple-server stations, and abandonments. Surprisingly, with abandonments, the optimality of JSQ for minimizing the number of customers in the system depends on the relative abandonment and service rates. We extend our model to finite buffers and resequencing. We assume exponential service. Our optimality results are very strong; we minimize the queue length process in the weak majorization sense.

We consider a Markov-modulated Brownian motion reflected to stay in a strip [0, B]. The stationary distribution of this process is known to have a simple form under some assumptions. We provide a short probabilistic argument leading to this result and explain its simplicity. Moreover, this argument allows for generalizations including the distribution of the reflected process at an independent, exponentially distributed epoch. Our second contribution concerns transient behavior of the model. We identify the joint law of the processes defining the model at inverse local times.

The leaky bucket is a flow control mechanism that is designed to reduce the effect of the inevitable variability in the input stream into a node of a communication network. In this paper we study what happens when an input stream with heavy-tailed work sessions arrives to a server protected by such a leaky bucket. Heavy-tailed sessions produce long-range dependence in the input stream. Previous studies of single server fluid queues without flow control suggested that such long-range dependence can have a dramatic effect on the system performance. By concentrating on the expected time till overflow of a large finite buffer we show that leaky-bucket flow control does make the system overflow less often, but long-range dependence still makes its presence felt.