scholarly journals Priority queueing model with balking and reneging

2010 ◽  
Vol 2 (1) ◽  
pp. 38-41
Author(s):  
Charan Jeet Singh
Keyword(s):  
Single Server ◽  
Queueing Model ◽  
Finite Difference Equation ◽  
Preemptive Priority ◽  
Balance Equations ◽  
Steady State Probability ◽  
Infinite Population ◽  
Level 1 ◽  
Number Of Customers ◽  
Priority Queueing

This investigation deals with two levels, single server preemptive priority queueing model with discouragement behaviour (balking and reneging) of customers. Arrivals to each level are assumed to follow a Poisson process and service times are exponentially distributed. The decision to balk / renege is made on the basis of queue length only. Two specific forms of balking behaviour are considered. The system under consideration is solved by using a finite difference equation approach for solving the governing balance equations of the queueing model, with infinite population of level 1 customer. The steady state probability distribution of the number of customers in the system is obtained.

scholarly journals A M/M/1 Queueing Network with Classical Retrial Policy

2021 ◽  
Vol 12 (1S) ◽  
pp. 329-337
Author(s):  
S. Shanmugasundaram, Et. al.
Keyword(s):  
Steady State ◽  
Queue Length ◽  
Queueing Network ◽  
State Probability ◽  
Queueing Model ◽  
Steady State Probability ◽  
Numerical Examples ◽  
System Length ◽  
Number Of Customers ◽  
Little's Formula

In this paper we study the M/M/1 queueing model with retrial on network. We derive the steady state probability of customers in the network, the average number of customers in the all the three nodes in the system, the queue length, system length using little’s formula. The particular case is derived (no retrial). The numerical examples are given to test the correctness of the model.

scholarly journals A discrete single server queue with Markovian arrivals and phase type group services

1995 ◽  
Vol 8 (2) ◽  
pp. 151-176 ◽  
Author(s):  
Attahiru Sule Alfa ◽  
K. Laurie Dolhun ◽  
S. Chakravarthy
Keyword(s):  
Steady State ◽  
Queueing System ◽  
State Probability ◽  
Arrival Process ◽  
Single Server ◽  
Probability Vector ◽  
Phase Type Distribution ◽  
Steady State Probability ◽  
Phase Type ◽  
Number Of Customers

We consider a single-server discrete queueing system in which arrivals occur according to a Markovian arrival process. Service is provided in groups of size no more than M customers. The service times are assumed to follow a discrete phase type distribution, whose representation may depend on the group size. Under a probabilistic service rule, which depends on the number of customers waiting in the queue, this system is studied as a Markov process. This type of queueing system is encountered in the operations of an automatic storage retrieval system. The steady-state probability vector is shown to be of (modified) matrix-geometric type. Efficient algorithmic procedures for the computation of the rate matrix, steady-state probability vector, and some important system performance measures are developed. The steady-state waiting time distribution is derived explicitly. Some numerical examples are presented.

scholarly journals TheN×D-BMAP/G/1 Queueing Model: Queue Contents and Delay Analysis

2011 ◽  
Vol 2011 ◽  
pp. 1-31 ◽  
Author(s):  
Bart Steyaert ◽  
Joris Walraevens ◽  
Dieter Fiems ◽  
Herwig Bruneel
Keyword(s):  
Closed Form ◽  
Customer Service ◽  
Probability Generating Function ◽  
Mean Value ◽  
Arrival Process ◽  
Single Server ◽  
Steady State Probability ◽  
Absolute Minimum ◽  
Number Of Customers ◽  
Customer Delay

We consider a single-server discrete-time queueing system with N sources, where each source is modelled as a correlated Markovian customer arrival process, and the customer service times are generally distributed. We focus on the analysis of the number of customers in the queue, the amount of work in the queue, and the customer delay. For each of these quantities, we will derive an expression for their steady-state probability generating function, and from these results, we derive closed-form expressions for key performance measures such as their mean value, variance, and tail distribution. A lot of emphasis is put on finding closed-form expressions for these quantities that reduce all numerical calculations to an absolute minimum.

scholarly journals A preemptive priority queue with a general bulk service rule

1986 ◽  
Vol 33 (2) ◽  
pp. 237-243 ◽  
Author(s):  
R. Sivasamy
Keyword(s):  
Queueing System ◽  
Priority Queue ◽  
Single Server ◽  
Preemptive Priority ◽  
Lower Priority ◽  
Bulk Service ◽  
Queue Lengths ◽  
The Mean ◽  
General Bulk Service Rule ◽  
Priority Queueing

In this paper a single server preemptive priority queueing system, consisting of two types of units, with unlimited Poisson inputs and exponential service time distributions, is studied. The higher priority units are served in batches according to a general bulk service rule and they have preemptive priority over lower priority units. Steady state queue length distributions, stability condition and the mean queue lengths are obtained.

scholarly journals Analysis of a multi-server queueing model of ABR

1998 ◽  
Vol 11 (3) ◽  
pp. 339-354 ◽  
Author(s):  
R. Núñez-Queija ◽  
O. J. Boxma
Keyword(s):  
Asynchronous Transfer Mode ◽  
Fixed Number ◽  
Atm Networks ◽  
Single Server ◽  
Queueing Model ◽  
Processor Sharing ◽  
Preemptive Priority ◽  
Transfer Mode ◽  
Multi Server ◽  
Channel Service

In this paper we present a queueing model for the performance analysis of Available Bit Rate (ABR) traffic in Asynchronous Transfer Mode (ATM) networks. We consider a multi-channel service station with two types of customers, denoted by high priority and low priority customers. In principle, high priority customers have preemptive priority over low priority customers, except on a fixed number of channels that are reserved for low priority traffic. The arrivals occur according to two independent Poisson processes, and service times are assumed to be exponentially distributed. Each high priority customer requires a single server, whereas low priority customers are served in processor sharing fashion. We derive the joint distribution of the numbers of customers (of both types) in the system in steady state. Numerical results illustrate the effect of high priority traffic on the service performance of low priority traffic.

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%.

Analysis of single server finite queueing model with reneging

2016 ◽  
Vol 9 (1) ◽  
pp. 15 ◽  
Author(s):  
Charan Jeet Singh ◽  
Madhu Jain ◽  
Binay Kumar
Keyword(s):  
Single Server ◽  
Queueing Model
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