In most of the service systems considered so far in queuing theory, no fresh customer is admitted to a batch undergoing when number less than threshold. However, few researchers case customers accessing ongoing batch, irrespective how long was provided that batch. A system with different kind accessibility relates real situation studied paper. Consider single server which process comprises k st...

In this paper, open queuing networks with Poisson arrivals and single-server infinite buffer queues are considered. Unlike traditional models, customers served (with exponential service time) in batches, so that the nodes non-work-conserving. The main contribution of work is design an efficient algorithm to find batch sizes which minimize average response time network. As preliminary steps at b...

A class of discrete-time priority queueing systems with Markov modulated arrivals is considered. In these systems, N queues are served by a single server according to priorities that are preassigned to the queues. Packet arrivals are modeled as discrete-time batch processes with a distribution that depends on the state of an independent common two-state Markov chain. This allows to cover a wide...

In this paper, we consider a special discrete-time queuing system with two head-of-line (HOL) priority queues and a mix of correlated and uncorrelated arrivals. The arrival process to the high priority queue is correlated and consists of a train of a fixed number of fixed-length packets, while the low priority traffic consists of batch arrivals that are independent and identically distributed f...

A new queue, referred to here as the HetSigma queue, in the Markovian framework, is proposed in order to model nodes in modern telecommunication networks. The queue has many of the necessary ingredients, such as joint (or individual) Markov modulation of the arrival and service processes, superposition of K CPP (compound Poisson process) streams of (positive) customer arrivals, and a CPP of neg...

Constant Bit Rate (CBR) traffic is expected to be an important source of traffic in high-speed networks. Such sources may have stringent delay and loss requirements and in many cases, they should be delivered exactly as they were generated. A simple delay priority scheme will bound the cell delay and jitter for CBR flows, so that in the network switches, CBR traffic will only compete with other...

Consider a single server fixed batch service queueing system under multiple vacation with a possibility of negative arrival in which the arrival rate λ follows a Poisson process, the service time follows an exponential distribution with parameter μ. Further we assume a negative arrival rate occur at the rate of ν which follows a Poisson process and the length of time the server in vacation foll...

1. The MM ∑K k=1 CPPk/GE/c/L G-Queue It is well known that the traffic in today’s telecommunication systems often exhibits burstiness i.e. batches of transmission units (e.g. packets) arrive together with correlation among the interarrival times [12]. Several models have been proposed to model such arrival-service processes, queues and networks. These include the compound Poisson process (CPP) ...

A single-server non-pre-emptive priority queueing system of a finite capacity with many types customers is analyzed. Inter-arrival times can be correlated and batch arrivals are allowed. Possible unreliability the server, implying loss customer or necessity its service from early beginning some phase service, taken into account. Initial priorities provided to various at arrival moment varied (i...