In this paper, we consider a discrete-time finite-buffer queue with correlated arrivals and service interruptions and the corresponding infinite-buffer queue. Under some assumptions, we derive an exact relation holding between the loss probability in the finite-buffer queue and the queue length distribution in the corresponding infinite-buffer queue. The exact relation is considered as an integ...

The probabilistic structure for the transient M/E,/2 queue is derived in discrete time, where El, denotes a k-Erlangdistribution. This queue has a twodimensional state-space. Expressions for the expected delay in queue are formulated in terms oftransition probabilities. Results are numerically evaluated for a few cases. The convergence behavior is similar to that seen in previous work on queues...

In this paper we study a single-server queue where the inter-arrival times and the service times depend on a common discrete time Markov Chain. This model generalizes the well-known MAP/G/1 queue by allowing dependencies between interarrival and service times. The waiting time process is directly analyzed by solving Lindley’s equation by transform methods. The Laplace Stieltjes transforms (LST)...

A novel approach for obtaining the response time in a discrete time tandem queue with blocking, using matrix analytic methods, is presented. The approach sets up the appropriate Markov chain based on the age of the leading customer in the first queue, together with other auxiliary variables. By this approach the response time is obtained with only minor additional effort after obtaining the sta...

In this paper we study a broad class of semi-Markovian queues introduced by Sengupta. This class contains many classical queues such as the GI/M/1 queue, SM/MAP/1 queue and others, as well as queues with correlated inter-arrival and service times. Queues belonging to this class are characterized by a set of matrices of size m and Sengupta showed that its waiting time distribution can be represe...

In this paper, we discuss the discrete-time Geom/G/1 queue with multiple adaptive vacations and server setup/closedown times. We consider two types of closedown time policies which differ from each other in the completion instant of the closedown times and contrast the effects of them on the queueing system. We derive the probability generating functions (PGFs) and stochastic decomposition resu...

We consider a discrete-time single-server queue with arrivals governed by a stationary Markov chain, where no arrivals are assumed to occur only when the Markov chain is in a particular state. This assumption implies that off-periods in the arrival process are i.i.d. and geometrically distributed. For this queue, we establish the exact relationship between queue length distributions in a finite...

It is well known that a simple relation called proportional relation holds for some queueing models, that is, the stationary queue length distribution of one system can be expressed as the product of a constant and the distribution of another system which is different only in the buffer capacity. Recently, the proportional relation has been verified for various discrete-time single-server queue...

In commonly used approaches for the discrete-time bulk service queue, the stationary queue length distribution follows from the roots inside or outside the unit circle of a characteristic equation. We present analytic representations of these roots in the form of sample values of periodic functions with analytically given Fourier series coefficients, making these approaches more transparent and...