Expected waiting times in a multiclass batch arrival retrial queue

1986 ◽  
Vol 23 (1) ◽  
pp. 144-154 ◽  
Author(s):  
V. G. Kulkarni
Keyword(s):  
Waiting Times ◽  
Retrial Queue ◽  
Batch Arrival ◽  
Single Server ◽  
Waiting Room ◽  
Compound Poisson ◽  
Special Cases

Expressions are derived for the expected waiting times for the customers of two types who arrive in batches (in a compound Poisson fashion) at a single-server queueing station with no waiting room. Those who cannot get served immediately keep returning to the system after random exponential amounts of time until they get served. The result is shown to agree with similar results for three special cases studied in the literature.

Expected waiting times in a multiclass batch arrival retrial queue

1986 ◽  
Vol 23 (01) ◽  
pp. 144-154 ◽  
Author(s):  
V. G. Kulkarni
Keyword(s):  
Waiting Times ◽  
Retrial Queue ◽  
Batch Arrival ◽  
Single Server ◽  
Waiting Room ◽  
Compound Poisson ◽  
Special Cases

Expressions are derived for the expected waiting times for the customers of two types who arrive in batches (in a compound Poisson fashion) at a single-server queueing station with no waiting room. Those who cannot get served immediately keep returning to the system after random exponential amounts of time until they get served. The result is shown to agree with similar results for three special cases studied in the literature.

scholarly journals Insensitive Bounds for the Stationary Distribution of a Single Server Retrial Queue with Server Subject to Active Breakdowns

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Mohamed Boualem
Keyword(s):  
Markov Chain ◽  
Stationary Distribution ◽  
Retrial Queue ◽  
Embedded Markov Chain ◽  
Single Server ◽  
Waiting Room ◽  
Monotonicity Properties

The paper addresses monotonicity properties of the single server retrial queue with no waiting room and server subject to active breakdowns. The obtained results allow us to place in a prominent position the insensitive bounds for the stationary distribution of the embedded Markov chain related to the model in the study. Numerical illustrations are provided to support the results.

A single-server queue with server vacations and a class of non-renewal arrival processes

1990 ◽  
Vol 22 (3) ◽  
pp. 676-705 ◽  
Author(s):  
David M. Lucantoni ◽  
Kathleen S. Meier-Hellstern ◽  
Marcel F. Neuts
Keyword(s):  
Waiting Times ◽  
Arrival Process ◽  
Single Server ◽  
Single Server Queue ◽  
Arbitrary Time ◽  
Markov Modulated Poisson Process ◽  
Special Cases ◽  
Server Queue ◽  
Arrival Processes ◽  
Markov Modulated

We study a single-server queue in which the server takes a vacation whenever the system becomes empty. The service and vacation times and the arrival process are all assumed to be mutually independent. The successive service times and the vacation times each form independent, identically distributed sequences with general distributions. A new class of non-renewal arrival processes is introduced. As special cases, it includes the Markov-modulated Poisson process and the superposition of phase-type renewal processes.Algorithmically tractable equations for the distributions of the waiting times at an arbitrary time and at arrivals, as well as for the queue length at an arbitrary time, at arrivals, and at departures are established. Some factorizations, which are known for the case of renewal input, are generalized to this new framework and new factorizations are obtained. The algorithmic implementation of these results is discussed.

scholarly journals On a multiclass batch arrival retrial queue

1988 ◽  
Vol 20 (02) ◽  
pp. 483-487 ◽  
Author(s):  
G. I. Falin
Keyword(s):  
Queueing System ◽  
Single Channel ◽  
Waiting Times ◽  
Retrial Queue ◽  
Batch Arrival

Kulkarni (1986) derived expressions for the expected waiting times for customers of two types who arrive in batches at a single-channel repeated orders queueing system. We propose another method of solving this problem and extend Kulkarni&s result to the case of N≧2 classes of customers.

scholarly journals A Batch Arrival Single Server Queue with Server Providing General Service in Two Fluctuating Modes and Reneging during Vacation and Breakdowns

2014 ◽  
Vol 2014 ◽  
pp. 1-12
Author(s):  
Monita Baruah ◽  
Kailash C. Madan ◽  
Tillal Eldabi
Keyword(s):  
Repair Process ◽  
Batch Arrival ◽  
Single Server ◽  
Single Server Queue ◽  
Numerical Illustration ◽  
Random Breakdown ◽  
Special Cases ◽  
Server Queue ◽  
Service Rates ◽  
General Service

We study the behavior of a batch arrival queuing system equipped with a single server providing general arbitrary service to customers with different service rates in two fluctuating modes of service. In addition, the server is subject to random breakdown. As soon as the server faces breakdown, the customer whose service is interrupted comes back to the head of the queue. As soon as repair process of the server is complete, the server immediately starts providing service in mode 1. Also customers waiting for service may renege (leave the queue) when there is breakdown or when server takes vacation. The system provides service with complete or reduced efficiency due to the fluctuating rates of service. We derive the steady state queue size distribution. Some special cases are discussed and numerical illustration is provided to see the effect and validity of the results.

Finite capacity vacation models with non-renewal input

1991 ◽  
Vol 28 (01) ◽  
pp. 174-197 ◽  
Author(s):  
C. Blondia
Keyword(s):  
Waiting Time ◽  
Time Distribution ◽  
Length Distribution ◽  
Time Instant ◽  
Arrival Process ◽  
Service Discipline ◽  
Single Server ◽  
Waiting Time Distribution ◽  
Waiting Room ◽  
Special Cases

This paper studies a single server queue with finite waiting room where the server takes vacations according to two different strategies: (i) an exhaustive service discipline, where the server takes a vacation whenever the system becomes empty and these vacations are repeated as long as there are no customers in the system upon return from a vacation, i.e. a repeated vacation strategy; (ii) a limited service discipline, where the server begins a vacation either if K customers have been served in the same busy period or if the system is empty and then a repeated vacation strategy is followed. The input process is a general Markovian arrival process introduced by Lucantoni, Meier-Hellstern and Neuts, which as special cases includes the Markov modulated Poisson process and the phase-type renewal process. The service times and vacation times each are generally distributed random variables. For both models, we obtain the queue length distribution at departures, at an arbitrary time instant and at arrival time. We also derive the loss probability of an arriving customer. We obtain formulae for the LST of the virtual waiting time distribution and for the LST of the waiting time distribution at arrival epochs.

Finite capacity vacation models with non-renewal input

1991 ◽  
Vol 28 (1) ◽  
pp. 174-197 ◽  
Author(s):  
C. Blondia
Keyword(s):  
Waiting Time ◽  
Time Distribution ◽  
Length Distribution ◽  
Time Instant ◽  
Arrival Process ◽  
Service Discipline ◽  
Single Server ◽  
Waiting Time Distribution ◽  
Waiting Room ◽  
Special Cases

This paper studies a single server queue with finite waiting room where the server takes vacations according to two different strategies: (i) an exhaustive service discipline, where the server takes a vacation whenever the system becomes empty and these vacations are repeated as long as there are no customers in the system upon return from a vacation, i.e. a repeated vacation strategy; (ii) a limited service discipline, where the server begins a vacation either if K customers have been served in the same busy period or if the system is empty and then a repeated vacation strategy is followed. The input process is a general Markovian arrival process introduced by Lucantoni, Meier-Hellstern and Neuts, which as special cases includes the Markov modulated Poisson process and the phase-type renewal process. The service times and vacation times each are generally distributed random variables. For both models, we obtain the queue length distribution at departures, at an arbitrary time instant and at arrival time. We also derive the loss probability of an arriving customer. We obtain formulae for the LST of the virtual waiting time distribution and for the LST of the waiting time distribution at arrival epochs.

scholarly journals On a multiclass batch arrival retrial queue

1988 ◽  
Vol 20 (2) ◽  
pp. 483-487 ◽  
Author(s):  
G. I. Falin
Keyword(s):  
Queueing System ◽  
Single Channel ◽  
Waiting Times ◽  
Retrial Queue ◽  
Batch Arrival

Kulkarni (1986) derived expressions for the expected waiting times for customers of two types who arrive in batches at a single-channel repeated orders queueing system. We propose another method of solving this problem and extend Kulkarni&s result to the case of N≧2 classes of customers.

A single-server queue with server vacations and a class of non-renewal arrival processes

1990 ◽  
Vol 22 (03) ◽  
pp. 676-705 ◽  
Author(s):  
David M. Lucantoni ◽  
Kathleen S. Meier-Hellstern ◽  
Marcel F. Neuts
Keyword(s):  
Waiting Times ◽  
Arrival Process ◽  
Single Server ◽  
Single Server Queue ◽  
Arbitrary Time ◽  
Markov Modulated Poisson Process ◽  
Special Cases ◽  
Server Queue ◽  
Arrival Processes ◽  
Markov Modulated

We study a single-server queue in which the server takes a vacation whenever the system becomes empty. The service and vacation times and the arrival process are all assumed to be mutually independent. The successive service times and the vacation times each form independent, identically distributed sequences with general distributions. A new class of non-renewal arrival processes is introduced. As special cases, it includes the Markov-modulated Poisson process and the superposition of phase-type renewal processes. Algorithmically tractable equations for the distributions of the waiting times at an arbitrary time and at arrivals, as well as for the queue length at an arbitrary time, at arrivals, and at departures are established. Some factorizations, which are known for the case of renewal input, are generalized to this new framework and new factorizations are obtained. The algorithmic implementation of these results is discussed.

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