G-networks are novel product form queuing networks that, in addition to ordinary customers, contain unusual entities such as “negative customers” which eliminate normal customers, and “triggers” that move other customers from some queue to another. Recently we introduced one more special type of customer, a “reset”, which may be sent out by any server at the end of a service epoch, and that wil...

We develop approximate solutions for the equilibrium queue length probability distribution of queues in open Markovian networks by considering each queue independently, constructing its arrival process as the join of each contributing queue's departing traffic. Without modulation and non-unit batches, we would only need to consider mean internal traffic rates, modelling each queue as M/M/1 to g...

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...

The “Horizontal Y” shaped queuing model in which there is bulk infinite arrival of patients, but available M services are limited. discrete flow patients the system reduced continuous and a diffusion equation used. In terms means variances inter-arrival time distribution, this process number servers used, imposing reflecting boundaries. inspiration for analysis came from Aradhye Kallurkar [2], ...

The public service sector is a that engaged to serve the interests of community. To get satisfies public, there needs be innovation in system renewal. Many factors need analyzed create satisfying service. One determining community satisfaction queuing area. Queue analysis an analytical method measure performance system. measured services includes number visitors entering queue and time customer...

Two approximate techniques for analyzing the window size distribution of TCP flows sharing a RED-like bottleneck queue are presented. Both methods presented first use a fixed point algorithm to obtain the mean window sizes of the flows, and the mean queue length in the bottleneck buffer. The simpler of the two methods then uses the ‘square root formula’ for TCP; the other method is more complic...

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) ...

1 Abstract We consider a single-server multi-queue system with unlimited-size batch service 1 where the next queue to be served is the one with the most senior customer (the so called 2 ‘Israeli Queue’). We study a Markovian system with state-dependent group-joining policy 3 and derive results for various performance measures, such as steady-state distribution of 4 the number of groups in the s...

The letter M stands for memoryless, i.e. the Poisson process with exponential distribution. Other possibilities include D for deterministic inter-arrival times, and G denoting a general distribution of inter-arrival times. Therefore, the M/M/1 queueing system consists of customers arriving according to a Poisson process with rate λ, and one server with a service time per customer that is expone...

In the literature, retrial queues with batch arrivals and heavy-tailed service times have been studied so-called equivalence theorem has established under condition that time is heavier than size. The provides distribution (or tail) between total number of customers in system for queue corresponding standard (non-retrial) queue. this paper, assumption regularly varying tails, we eliminate by al...