Computation of the stationary distribution of the queue size in an M/G/1 queueing system with variable service rate

1980 ◽  
Vol 17 (02) ◽  
pp. 515-522 ◽  
Author(s):  
A. Federgruen ◽  
H. C. Tijms
Keyword(s):  
Stationary Distribution ◽  
Queueing System ◽  
Computational Approach ◽  
Service Rate ◽  
Queue Size ◽  
Stationary Probabilities

This paper presents a simple and computationally tractable method which recursively computes the stationary probabilities of the queue size in an M/G/1 queueing system with variable service rate. For each service two possible service types are available and the service rule is characterized by two switch-over levels. The computational approach discussed in this paper can be applied to a variety of queueing problems.

Computation of the stationary distribution of the queue size in an M/G/1 queueing system with variable service rate

1980 ◽  
Vol 17 (2) ◽  
pp. 515-522 ◽  
Author(s):  
A. Federgruen ◽  
H. C. Tijms
Keyword(s):  
Stationary Distribution ◽  
Queueing System ◽  
Computational Approach ◽  
Service Rate ◽  
Queue Size ◽  
Stationary Probabilities

This paper presents a simple and computationally tractable method which recursively computes the stationary probabilities of the queue size in an M/G/1 queueing system with variable service rate. For each service two possible service types are available and the service rule is characterized by two switch-over levels. The computational approach discussed in this paper can be applied to a variety of queueing problems.

On a Markovian queue with weakly correlated interarrival times

1981 ◽  
Vol 18 (01) ◽  
pp. 190-203 ◽  
Author(s):  
Guy Latouche
Keyword(s):  
Time Distribution ◽  
Queueing System ◽  
Interarrival Time ◽  
Probability Vector ◽  
Common Value ◽  
Markovian Queue ◽  
The Stability ◽  
Number Of Customers ◽  
Stationary Probabilities ◽  
Stationary Probability Vector

A queueing system with exponential service and correlated arrivals is analysed. Each interarrival time is exponentially distributed. The parameter of the interarrival time distribution depends on the parameter for the preceding arrival, according to a Markov chain. The parameters of the interarrival time distributions are chosen to be equal to a common value plus a factor ofε, where ε is a small number. Successive arrivals are then weakly correlated. The stability condition is found and it is shown that the system has a stationary probability vector of matrix-geometric form. Furthermore, it is shown that the stationary probabilities for the number of customers in the system, are analytic functions ofε, for sufficiently smallε, and depend more on the variability in the interarrival time distribution, than on the correlations.

The single-server queue with service depending on queue size and with the preemptive-resume last-come–first-served queue discipline

1987 ◽  
Vol 24 (03) ◽  
pp. 758-767
Author(s):  
D. Fakinos
Keyword(s):  
Queueing System ◽  
Limiting Distribution ◽  
Single Server ◽  
Queue Size ◽  
Single Server Queue ◽  
Preemptive Resume ◽  
Server Queue ◽  
Queue Discipline ◽  
Service Times

This paper studies theGI/G/1 queueing system assuming that customers have service times depending on the queue size and also that they are served in accordance with the preemptive-resume last-come–first-served queue discipline. Expressions are given for the limiting distribution of the queue size and the remaining durations of the corresponding services, when the system is considered at arrival epochs, at departure epochs and continuously in time. Also these results are applied to some particular cases of the above queueing system.

scholarly journals Simulation and Analysis of Impact of Buffering of Voice Calls in Integrated Voice and Data Communication System

2012 ◽  
pp. 112-116
Author(s):  
V M. Chavan ◽  
M M. Kuber ◽  
R J. Mukhedkar
Keyword(s):  
Communication System ◽  
Queuing Theory ◽  
Data Communication ◽  
Service Rate ◽  
Queue Size ◽  
Markov Chain Analysis ◽  
Chain Analysis ◽  
Voice Calls ◽  
The Impact ◽  
The Voice

Queuing theory and Markov chain analysis plays vital role in analyzing real-life problems. It is applied to wired network, wireless network and mobile communication to analyze the packet traffic in packet switched network. In this simulation and analysis, integrated communication system such as voice and data is simulated with different queue size for voice calls with different arrival and service rate and its results are analyzed to study the impact of buffering of voice and data calls for the proposed integrated wired network using Queuing theory and Markov chain analysis. We also propose to optimize the system characteristics in an attempt to provide better Quality of Service (QoS) for systems with integrated voice and data calls. The proposed models have two traffic flow namely voice calls (real-time traffic like audio) and data calls (data traffic like FTP). A single channel is assigned for voice and data calls. The incoming voice and data calls are queued when the channel is busy. Voice calls are delay-sensitive therefore priority is assigned to Constant Bit Rate (CBR) traffic voice request. For such systems, it is important to analyze the impact of buffering the voice calls as well as data calls for various mean arrival rates and mean service times for voice and data call requests. The impact of buffering the voice calls with different queue size, mean arrival rates and service rate are analyzed. These results of dedicated integrated voice and data communication system can be used for simulating any type of wired network. The minimum buffer or jitter required for both the traffic is calculated using Packet Delivery Fraction (PDF).

Optimal Thresholds of an Infinite Buffer Discrete-Time Two-Server System with Triadic Policy

2011 ◽  
Vol 2 (4) ◽  
pp. 75-88
Author(s):  
Veena Goswami ◽  
G. B. Mund
Keyword(s):  
Discrete Time ◽  
Queueing System ◽  
Minimum Cost ◽  
Service Rate ◽  
Closed Form Solutions ◽  
Optimal Thresholds ◽  
Optimal Service ◽  
Number Of Customers ◽  
System Operating ◽  
Server System

This paper analyzes a discrete-time infinite-buffer Geo/Geo/2 queue, in which the number of servers can be adjusted depending on the number of customers in the system one at a time at arrival or at service completion epoch. Analytical closed-form solutions of the infinite-buffer Geo/Geo/2 queueing system operating under the triadic (0, Q N, M) policy are derived. The total expected cost function is developed to obtain the optimal operating (0, Q N, M) policy and the optimal service rate at minimum cost using direct search method. Some performance measures and sensitivity analysis have been presented.

Perturbation bounds for the stationary probabilities of a finite Markov chain

1984 ◽  
Vol 16 (04) ◽  
pp. 804-818 ◽  
Author(s):  
Moshe Haviv ◽  
Ludo Van Der Heyden
Keyword(s):  
Markov Chain ◽  
Stationary Distribution ◽  
Finite Markov Chain ◽  
Perturbation Bounds ◽  
Aggregation Technique ◽  
Stationary Probabilities

This paper discusses perturbation bounds for the stationary distribution of a finite indecomposable Markov chain. Existing bounds are reviewed. New bounds are presented which more completely exploit the stochastic features of the perturbation and which also are easily computable. Examples illustrate the tightness of the bounds and their application to bounding the error in the Simon–Ando aggregation technique for approximating the stationary distribution of a nearly completely decomposable Markov chain.

A stable algorithm for stationary distribution calculation for a BMAP/SM/1 queueing system with Markovian arrival input of disasters

2004 ◽  
Vol 41 (02) ◽  
pp. 547-556 ◽  
Author(s):  
Alexander Dudin ◽  
Olga Semenova
Keyword(s):  
Markov Chain ◽  
Stationary State ◽  
Stationary Distribution ◽  
Queueing System ◽  
Embedded Markov Chain ◽  
State Distribution ◽  
Stable Algorithm ◽  
Distribution Calculation

Disaster arrival into a queueing system causes all customers to leave the system instantaneously. We present a numerically stable algorithm for calculating the stationary state distribution of an embedded Markov chain for the BMAP/SM/1 queue with a MAP input of disasters.

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