Finite Queues at the Limit of Saturation

2012 ◽  
Author(s):  
Miklos Telek ◽  
Miklos Vecsei
Keyword(s):  
Finite Queues

Algorithmic Approach to Analysis of Queuing System with Finite Queues and Jump-like Priorities

2012 ◽  
Vol 44 (12) ◽  
pp. 43-54 ◽  
Author(s):  
Agasi Zarbali ogly Melikov ◽  
Leonid A. Ponomarenko ◽  
Che Soong Kim
Keyword(s):  
Queuing System ◽  
Algorithmic Approach ◽  
Finite Queues

scholarly journals A Taylor Series Approach for Service-Coupled Queueing Systems with Intermediate Load

2017 ◽  
Vol 2017 ◽  
pp. 1-10 ◽  
Author(s):  
Ekaterina Evdokimova ◽  
Sabine Wittevrongel ◽  
Dieter Fiems
Keyword(s):  
Performance Measures ◽  
Queueing Systems ◽  
Poisson Processes ◽  
Series Expansions ◽  
Service Rate ◽  
Single Server ◽  
Queueing Model ◽  
State Space Explosion ◽  
Finite Queues ◽  
Service Rates

This paper investigates the performance of a queueing model with multiple finite queues and a single server. Departures from the queues are synchronised or coupled which means that a service completion leads to a departure in every queue and that service is temporarily interrupted whenever any of the queues is empty. We focus on the numerical analysis of this queueing model in a Markovian setting: the arrivals in the different queues constitute Poisson processes and the service times are exponentially distributed. Taking into account the state space explosion problem associated with multidimensional Markov processes, we calculate the terms in the series expansion in the service rate of the stationary distribution of the Markov chain as well as various performance measures when the system is (i) overloaded and (ii) under intermediate load. Our numerical results reveal that, by calculating the series expansions of performance measures around a few service rates, we get accurate estimates of various performance measures once the load is above 40% to 50%.

scholarly journals On the total loss probability of service stages in series

1990 ◽  
Vol 22 (1) ◽  
pp. 260-262
Author(s):  
P.-J. Courtois
Keyword(s):  
Simple Model ◽  
Loss Rate ◽  
Loss Probability ◽  
Total Loss ◽  
Finite Queues ◽  
In Series

The problem addressed here is related to the minimization of the total loss probability in series of finite queues at which customers are rejected if the waiting capacity is exceeded. More precisely, one is concerned with the question of determining whether or not there may exist conditions under which an increase of the loss rate at one queue, e.g. at the most upstream one, could result in a decrease of the total loss rate throughout the whole network. The answer obtained in the context of a simple model is negative.

System States for a Series of Finite Queues

1972 ◽  
Vol 20 (6) ◽  
pp. 1137-1141 ◽  
Author(s):  
Brian J. Haydon
Keyword(s):  
Finite Queues ◽  
System States

Two finite queues and their duals

1973 ◽  
Vol 5 (01) ◽  
pp. 22-24
Author(s):  
P. B. M. Roes
Keyword(s):  
Finite Queues

scholarly journals Stochastic and substochastic solutions for infinite-state Markov chains with applications to matrix-analytic methods

2008 ◽  
Vol 40 (04) ◽  
pp. 1157-1173
Author(s):  
Winfried K. Grassmann ◽  
Javad Tavakoli
Keyword(s):  
Markov Chain ◽  
Markov Chains ◽  
Transition Matrices ◽  
Matrix Analytic Methods ◽  
Analytic Methods ◽  
Finite Queues ◽  
Qbd Processes ◽  
Stochastic Solution ◽  
Number Of Visits ◽  
Infinite State

This paper deals with censoring of infinite-state banded Markov chains. Censoring involves reducing the time spent in states outside a certain set of states to 0 without affecting the number of visits within this set. We show that, if all states are transient, there is, besides the standard censored Markov chain, a nonstandard censored Markov chain which is stochastic. Both the stochastic and the substochastic solutions are found by censoring a sequence of finite transition matrices. If all matrices in the sequence are stochastic, the stochastic solution arises in the limit, whereas the substochastic solution arises if the matrices in the sequence are substochastic. We also show that, if the Markov chain is recurrent, the only solution is the stochastic solution. Censoring is particularly fruitful when applied to quasi-birth-and-death (QBD) processes. It turns out that key matrices in such processes are not unique, a fact that has been observed by several authors. We note that the stochastic solution is important for the analysis of finite queues.

scholarly journals Two parallel finite queues with simultaneous services and Markovian arrivals

1997 ◽  
Vol 10 (4) ◽  
pp. 383-405 ◽  
Author(s):  
S. R. Chakravarthy ◽  
S. Thiagarajan
Keyword(s):  
Markov Process ◽  
Performance Measures ◽  
System Performance ◽  
Arrival Process ◽  
Single Server ◽  
Queueing Model ◽  
Finite Capacity ◽  
Numerical Examples ◽  
Finite Queues ◽  
Large State Space

In this paper, we consider a finite capacity single server queueing model with two buffers, A and B, of sizes K and N respectively. Messages arrive one at a time according to a Markovian arrival process. Messages that arrive at buffer A are of a different type from the messages that arrive at buffer B. Messages are processed according to the following rules: 1. When buffer A(B) has a message and buffer B(A) is empty, then one message from A(B) is processed by the server. 2. When both buffers, A and B, have messages, then two messages, one from A and one from B, are processed simultaneously by the server. The service times are assumed to be exponentially distributed with parameters that may depend on the type of service. This queueing model is studied as a Markov process with a large state space and efficient algorithmic procedures for computing various system performance measures are given. Some numerical examples are discussed.

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