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...

This paper analyzes a renewal input  working vacations queue with change over times and Bernoulli schedulevacation interruption under (a,c,b) policy.The service and vacation times are exponentially distributed.The server begins service if there are at least c units in the queue and the service takes place in batches with a minimum of size a and a maximum of size b (a

The sensitivity of the performance measures such as the mean and the standard deviation of the queue length and the blocking probability with respect to the moments of the service time are numerically investigated. The steady state distribution of M/G/c queue is approximated by that of the M/PH/c queue where the phase type (PH) distribution is fitted by matching the first three moments of the s...

In this paper we consider a queuing system in which the service times of customers are independent and identically distributed random variables, the arrival process is stationary and has the property of orderliness, and the queue discipline is arbitrary. For this queuing system we obtain the steady state second moment of the queue size in terms of the stationary waiting time distribution of a s...

In this paper, a markovian queue with two types of servers and buffer space is considered. The resequencing constraint is imposed according to which the customers leave the system in the same order in which they entered it. For finite buffer queue, the steady state queue size distribution has been obtained.? 

| We present simple exponential approximations to the transient behavior of the stable M=M=1 queue. The approximations are optimal in a least-squares sense, and we nd them to agree well with exact results. Our approach can be used to derive approximations for any time-dependent quantity with a known Laplace transform, e.g., the probability distribution and the moments of the queue size, of the ...

A sensitivity analysis of a single-server, infinite-buffer queue with correlated arrivals and correlated service times is performed. We study and compare the isolated impact of (normalized) marginal moments and (normalized) correlation structures of the arrival and service processes on the performance measures of such a queue. For these correlated processes, we use Markovian arrival processes o...

The machine repair problem with spares and additional repairman is analyzed. The interfailure and repair times of the units are general identical and independently distributed. The failure and repair rates are assumed to be state dependent. Using diffusion approximation technique, we obtain the queue size distribution under steady state. The average number of failed units, average number of ope...

Scalable TCP [2] is a proposition for a new TCP where both the increase and the decrease rate of the window size are multiplicative. It has been recently proposed in order to improve performance in high speed networks. In this paper, we present a mathematical analysis of such multiplicative increase multiplicative decrease protocols in the presence of random losses. These are typical to wireles...