Abstract: We consider a finite-buffer single server queue with single (multiple) vacation(s) under batch Markovian Arrival Process (BMAP). The service discipline is varying number limited service, also called E-limited with limit variation (ELV) where the server serves until either the system is emptied or a randomly chosen limit of l customers have been served. Queue length distributions at va...

We consider a finite buffer queue with one deterministic server fed by packets arriving in batches. We assume that we are not able to fully describe the batch distribution: only the maximal size and the average number of packets are supposed known. Indeed, these two quantities are simple to measure in a real system. We additionally allow the batch distribution to be state dependent. We analyze ...

Petri nets are suitable for modelling of discrete-event systems with highly parallel and cooperating activities. In complex man-made systems, such as manufacturing systems, the systems’ specific properties, such as conflicts, deadlocks, limited buffer sizes, and finite resource constraints can be easily represented in the Petri net model. Therefore teaching of Petri net basics is an inevitable ...

Consider a single server queue with i.i.d. arrival and service processes, {A, An,n > 0} and {C, Cn,n > 0}, respectively, and a finite buffer B. The queue content process {Qn , n > 0} is recursively defined as Qn+1 = min((Qn + An+1 − Cn+1),B), q = max(0, q). When E(A−C) < 0, and A has a subexponential distribution, we show that the stationary expected loss rate for this queue E(Qn +An+1−Cn+1−B) ...

This paper analyzes a discrete-time finite-buffer multi-server bulk-service queueing system in which the interarrival-and service-times are, respectively, arbitrarily and geometrically distributed. Using the supplementary variable and the imbedded Markov-chain techniques, the queue is analyzed for the early arrival system. We obtain state probabilities at prearrival, arbitrary and outside obser...

In this paper, we investigate the variation in the reusable rate of cores (used products) on the performance of the remanufacturing system. The remanufacturing system considered here consists of three modules; viz., the disassembly and testing module for returned products, the disposition module for non-reusable returns, and the remanufacturing module. Each server in the system is subject to br...

This paper studies a fluid queueing system that has a single server, a single finite buffer, and which applies a strict priority discipline to multiple arriving streams of different classes. The arriving streams are modeled by statistically independent, identically distributed random processes. A proof is presented for the highly intuitive result that, in such a queueing system, a higher priori...

The bandwidth-intensive and long-lived nature of high quality digital video make it a challenging problem to transmit such video over the Internet. In this paper, we consider the problem of streaming a set of popular videos from a remote server to a large number of asynchronous clients, while making efficient use of network bandwidth, and still allowing clients to start instantaneous playback. ...

In this paper we have proposed a dynamic buffer allocation algorithm for the prefix, based on the popularity of the videos. More cache blocks are allocated for most popular videos and a few cache blocks are allocated for less popular videos. Buffer utilization is also maximized irrespective of the load on the Video-on-Demand system. Overload can lead the server getting slowed down. By storing t...

We give sufficient conditions under which a policy that assigns customers to the Fastest Available Server, labelled FAS, is optimal in queueing models with multiple independent Poisson arrival processes and heterogeneous parallel exponential servers. The criterion is to minimize the long-run average cost per unit time. We obtain results for loss models and for queueing systems with a finite-cap...