scholarly journals FINITE TWO LAYERED QUEUEING SYSTEMS

2016 ◽  
Vol 30 (3) ◽  
pp. 492-513 ◽  
Author(s):  
Efrat Perel ◽  
Uri Yechiali
Keyword(s):  
Waiting Times ◽  
Queueing Systems ◽  
Service Rate ◽  
Dimensional System ◽  
Single Server ◽  
Matrix Analytic Methods ◽  
Birth And Death Processes ◽  
Operating Modes ◽  
Loss Probabilities ◽  
Steady State Probabilities

We study layered queueing systems comprised two interlacing finite M/M/• type queues, where users of each layer are the servers of the other layer. Examples can be found in file sharing programs, SETI@home project, etc. Let Li denote the number of users in layer i, i=1, 2. We consider the following operating modes: (i) All users present in layer i join forces together to form a single server for the users in layer j (j≠i), with overall service rate μjLi (that changes dynamically as a function of the state of layer i). (ii) Each of the users present in layer i individually acts as a server for the users in layer j, with service rate μj.These operating modes lead to three different models which we analyze by formulating them as finite level-dependent quasi birth-and-death processes. We derive a procedure based on Matrix Analytic methods to derive the steady state probabilities of the two dimensional system state. Numerical examples, including mean queue sizes, mean waiting times, covariances, and loss probabilities, are presented. The models are compared and their differences are discussed.

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%.

A solvable model for a finite-capacity queueing system

1985 ◽  
Vol 22 (4) ◽  
pp. 903-911 ◽  
Author(s):  
V. Giorno ◽  
C. Negri ◽  
A. G. Nobile
Keyword(s):  
Queueing System ◽  
Waiting Times ◽  
Queueing Systems ◽  
Solvable Model ◽  
Probability Density Functions ◽  
Single Server ◽  
Finite Capacity ◽  
System Service ◽  
Transient Probabilities ◽  
Number Of Customers

Single–server–single-queue–FIFO-discipline queueing systems are considered in which at most a finite number of customers N can be present in the system. Service and arrival rates are taken to be dependent upon that state of the system. Interarrival intervals, service intervals, waiting times and busy periods are studied, and the results obtained are used to investigate the features of a special queueing model characterized by parameters (λ (Ν –n), μn). This model retains the qualitative features of the C-model proposed by Conolly [2] and Chan and Conolly [1]. However, quite unlike the latter, it also leads to closed-form expressions for the transient probabilities, the interarrival and service probability density functions and their moments, as well as the effective interarrival and service densities and their moments. Finally, some computational results are given to compare the model discussed in this paper with the C-model.

scholarly journals Markovian Queueing System with Discouraged Arrivals and Self-Regulatory Servers

2016 ◽  
Vol 2016 ◽  
pp. 1-11 ◽  
Author(s):  
K. V. Abdul Rasheed ◽  
M. Manoharan
Keyword(s):  
Queueing System ◽  
Queueing Systems ◽  
Single Server ◽  
Expected Number ◽  
Multiple Servers ◽  
Special Cases ◽  
Service Rates ◽  
Expected Waiting Time ◽  
Number Of Customers ◽  
Steady State Probabilities

We consider discouraged arrival of Markovian queueing systems whose service speed is regulated according to the number of customers in the system. We will reduce the congestion in two ways. First we attempt to reduce the congestion by discouraging the arrivals of customers from joining the queue. Secondly we reduce the congestion by introducing the concept of service switches. First we consider a model in which multiple servers have three service ratesμ1,μ2, andμ(μ1≤μ2<μ), say, slow, medium, and fast rates, respectively. If the number of customers in the system exceeds a particular pointK1orK2, the server switches to the medium or fast rate, respectively. For this adaptive queueing system the steady state probabilities are derived and some performance measures such as expected number in the system/queue and expected waiting time in the system/queue are obtained. Multiple server discouraged arrival model having one service switch and single server discouraged arrival model having one and two service switches are obtained as special cases. A Matlab program of the model is presented and numerical illustrations are given.

Closed queueing networks with blocking-a model for flexible manufacturing systems

1984 ◽  
Vol 16 (1) ◽  
pp. 9-9
Author(s):  
David D. W. Yao ◽  
J.A. Buzacott
Keyword(s):  
Flexible Manufacturing ◽  
Queueing Networks ◽  
Manufacturing Systems ◽  
Waiting Times ◽  
Queueing Systems ◽  
Priority Queue ◽  
Single Server ◽  
Closed Queueing Networks ◽  
State Behavior ◽  
Dynamic Priority

We consider a family of single-server queueing systems with two priority classes. The system operates under a dynamic priority queue discipline in which the relative priorities of customers increase with their waiting times, and which can be characterized by the urgency number. We investigate the transient as well as the steady-state behavior of the virtual waiting times of the two classes of customer as functions of the urgency number. Stochastic orderings, the joint distribution, and surprising limit results for these processes are obtained for the first time.

A solvable model for a finite-capacity queueing system

1985 ◽  
Vol 22 (04) ◽  
pp. 903-911 ◽  
Author(s):  
V. Giorno ◽  
C. Negri ◽  
A. G. Nobile
Keyword(s):  
Queueing System ◽  
Waiting Times ◽  
Queueing Systems ◽  
Solvable Model ◽  
Probability Density Functions ◽  
Single Server ◽  
Finite Capacity ◽  
System Service ◽  
Transient Probabilities ◽  
Number Of Customers

Single–server–single-queue–FIFO-discipline queueing systems are considered in which at most a finite number of customers N can be present in the system. Service and arrival rates are taken to be dependent upon that state of the system. Interarrival intervals, service intervals, waiting times and busy periods are studied, and the results obtained are used to investigate the features of a special queueing model characterized by parameters (λ (Ν –n), μn). This model retains the qualitative features of the C-model proposed by Conolly [2] and Chan and Conolly [1]. However, quite unlike the latter, it also leads to closed-form expressions for the transient probabilities, the interarrival and service probability density functions and their moments, as well as the effective interarrival and service densities and their moments. Finally, some computational results are given to compare the model discussed in this paper with the C-model.

scholarly journals The Correlation Coefficients of the Queue Lengths of Some Stationary Single Server Queues

1971 ◽  
Vol 12 (1) ◽  
pp. 35-46 ◽  
Author(s):  
A. G. Pakes
Keyword(s):  
Queue Length ◽  
Final Section ◽  
Waiting Times ◽  
Queueing Systems ◽  
Correlation Coefficients ◽  
Second Order ◽  
Single Server ◽  
Bulk Service ◽  
Queue Lengths ◽  
Queueing Processes

Until recently there has been little systematic work on the second-order properties of queueing processes. The aim of this paper is to study systematically the second-order properties of the queue length processes embedded at departure epochs in the M/G/1 and bulk service M/G/1 queues, and at arrival epochs in the GI/M/1 queue. In the latter case our results extend those of Daley [7], while in the ordinary M/G/1 queue our work parallels Daley's [6] discussion of waiting times in the same system. In the final section we briefly discuss two discrete time queueing systems.

A family of delay-dependent dynamic priority queueing systems

1984 ◽  
Vol 16 (1) ◽  
pp. 9-9
Author(s):  
P. K. Reeser
Keyword(s):  
Waiting Times ◽  
Queueing Systems ◽  
Priority Queue ◽  
Single Server ◽  
State Behavior ◽  
Dynamic Priority ◽  
Queue Discipline ◽  
Delay Dependent ◽  
First Time ◽  
Priority Queueing

We consider a family of single-server queueing systems with two priority classes. The system operates under a dynamic priority queue discipline in which the relative priorities of customers increase with their waiting times, and which can be characterized by the urgency number. We investigate the transient as well as the steady-state behavior of the virtual waiting times of the two classes of customer as functions of the urgency number. Stochastic orderings, the joint distribution, and surprising limit results for these processes are obtained for the first time.

Comparing Short and Long-Memory Charts to Monitor the Traffic Intensity of Single Server Queues

2019 ◽  
Vol 34 (1) ◽  
pp. 9-18
Author(s):  
Marta Santos ◽  
Manuel Cabral Morais ◽  
António Pacheco
Keyword(s):  
Long Memory ◽  
Control Charts ◽  
Performance Metrics ◽  
Waiting Times ◽  
Queueing Systems ◽  
Transportation Systems ◽  
Single Server ◽  
Traffic Intensity ◽  
Cusum Charts ◽  
Short Memory

Abstract The traffic intensity (ρ) is a vital parameter of queueing systems because it is a measure of the average occupancy of a server. Consequently, it influences their operational performance, namely queue lengths and waiting times. Moreover, since many computer, production and transportation systems are frequently modelled as queueing systems, it is crucial to use control charts to detect changes in ρ. In this paper, we pay particular attention to control charts meant to detect increases in the traffic intensity, namely: a short-memory chart based on the waiting time of the n-th arriving customer; two long-memory charts with more sophisticated control statistics, and the two cumulative sum (CUSUM) charts proposed by Chen and Zhou (2015). We confront the performances of these charts in terms of some run length related performance metrics and under different out-of-control scenarios. Extensive results are provided to give the quality control practitioner a concrete idea about the performance of these charts.

Sign in / Sign up

Export Citation Format

Share Document