scholarly journals A single server queue under random vacation policy

2019 ◽  
Author(s):  
Priyanka kalita ◽  
Gautam Choudhury
Keyword(s):  
Steady State ◽  
Lower Cost ◽  
Queueing System ◽  
System Size ◽  
Mean Value ◽  
Single Server ◽  
Idle Period ◽  
System A ◽  
Server Queue ◽  
Number Of Customers

This paper deals with an M/G/1 queueing system with random vacation policy, in which the server takes the maximum number of random vacations till it finds minimum one message (customer) waiting in a queue at a vacation completion epoch. If no arrival occurs after completing maximum number of random vacations, the server stays dormant in the system and waits for the upcoming arrival. Here, we obtain steady state queue size distribution at an idle period completion epoch and service completion epoch. We also obtain the steady state system size probabilities and system state probabilities. Some significant measures such as a mean number of customers served during the busy period, Laplace-Stieltjes transform of unfinished work and its corresponding mean value and second moment have been obtained for the system. A cost optimal policy have been developed in terms of the average cost function to determine a locally optimal random vacation policy at a lower cost. Finally, we present various numerical results for the above system performance measures.

A single server Markovian queuing system with limited buffer and reverse balking

2021 ◽  
Vol 12 (7) ◽  
pp. 1774-1784
Author(s):  
Girin Saikia ◽  
Amit Choudhury
Keyword(s):  
Steady State ◽  
Performance Measures ◽  
Mutual Fund ◽  
System Size ◽  
Queuing System ◽  
Single Server ◽  
Insurance Company ◽  
Number Of Customers ◽  
Steady State Probabilities

The phenomena are balking can be said to have been observed when a customer who has arrived into queuing system decides not to join it. Reverse balking is a particular type of balking wherein the probability that a customer will balk goes down as the system size goes up and vice versa. Such behavior can be observed in investment firms (insurance company, Mutual Fund Company, banks etc.). As the number of customers in the firm goes up, it creates trust among potential investors. Fewer customers would like to balk as the number of customers goes up. In this paper, we develop an M/M/1/k queuing system with reverse balking. The steady-state probabilities of the model are obtained and closed forms of expression of a number of performance measures are derived.

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.

Steady state solution of a single-server queue with linear repeated requests

1997 ◽  
Vol 34 (01) ◽  
pp. 223-233 ◽  
Author(s):  
J. R. Artalejo ◽  
A. Gomez-Corral
Keyword(s):  
Steady State ◽  
Hypergeometric Functions ◽  
Queueing Systems ◽  
General Setting ◽  
Steady State Solution ◽  
Single Server ◽  
Service Time Distribution ◽  
Steady State Distribution ◽  
Server Queue ◽  
Number Of Customers

Queueing systems with repeated requests have many useful applications in communications and computer systems modeling. In the majority of previous work the repeat requests are made individually by each unsatisfied customer. However, there is in the literature another type of queueing situation, in which the time between two successive repeated attempts is independent of the number of customers applying for service. This paper deals with the M/G/1 queue with repeated orders in its most general setting, allowing the simultaneous presence of both types of repeat requests. We first study the steady state distribution and the partial generating functions. When the service time distribution is exponential we show that the performance characteristics can be expressed in terms of hypergeometric functions.

scholarly journals Steady-State Analysis of a Flexible Markovian Queue with Server Breakdowns

Entropy ◽  
2019 ◽  
Vol 21 (3) ◽  
pp. 259 ◽  
Author(s):  
Messaoud Bounkhel ◽  
Lotfi Tadj ◽  
Ramdane Hedjar
Keyword(s):  
Steady State ◽  
Probability Generating Function ◽  
Threshold Level ◽  
System Size ◽  
Single Server ◽  
Markovian Queue ◽  
Breakdown Rates ◽  
Bulk Service ◽  
Service Rates ◽  
Number Of Customers

A flexible single-server queueing system is considered in this paper. The server adapts to the system size by using a strategy where the service provided can be either single or bulk depending on some threshold level c. If the number of customers in the system is less than c, then the server provides service to one customer at a time. If the number of customers in the system is greater than or equal to c, then the server provides service to a group of c customers. The service times are exponential and the service rates of single and bulk service are different. While providing service to either a single or a group of customers, the server may break down and goes through a repair phase. The breakdowns follow a Poisson distribution and the breakdown rates during single and bulk service are different. Also, repair times are exponential and repair rates during single and bulk service are different. The probability generating function and linear operator approaches are used to derive the system size steady-state probabilities.

On the single-server queue with the preemptive-resume last-come–first-served queue discipline

1986 ◽  
Vol 23 (01) ◽  
pp. 243-248
Author(s):  
D. Fakinos
Keyword(s):  
Equilibrium Distribution ◽  
Queueing System ◽  
Independent Random Variables ◽  
Single Server ◽  
Queue Size ◽  
Single Server Queue ◽  
Idle Period ◽  
Preemptive Resume ◽  
Server Queue ◽  
Queue Discipline

The paper considers the GI/G/1 queueing system under the assumption of a last-come–first-served queue discipline, where each customer begins service immediately upon his arrival. At the next arrival, the previous service is interrupted but no loss of service is involved. It has been shown that when the system is considered exclusively at arrival epochs or exclusively at departure epochs, then the equilibrium distribution of the queue-size is geometric, while the remaining durations of the corresponding services are independent random variables each one distributed as the idle period in the dual (inverse) queue. In this paper alternative simpler proofs of the above results are given.

Steady state solution of a single-server queue with linear repeated requests

1997 ◽  
Vol 34 (1) ◽  
pp. 223-233 ◽  
Author(s):  
J. R. Artalejo ◽  
A. Gomez-Corral
Keyword(s):  
Steady State ◽  
Hypergeometric Functions ◽  
Queueing Systems ◽  
General Setting ◽  
Steady State Solution ◽  
Single Server ◽  
Service Time Distribution ◽  
Steady State Distribution ◽  
Server Queue ◽  
Number Of Customers

Queueing systems with repeated requests have many useful applications in communications and computer systems modeling. In the majority of previous work the repeat requests are made individually by each unsatisfied customer. However, there is in the literature another type of queueing situation, in which the time between two successive repeated attempts is independent of the number of customers applying for service. This paper deals with the M/G/1 queue with repeated orders in its most general setting, allowing the simultaneous presence of both types of repeat requests. We first study the steady state distribution and the partial generating functions. When the service time distribution is exponential we show that the performance characteristics can be expressed in terms of hypergeometric functions.

An Unreliable Quorum Queueing System with Single and Multiple Vacations

2017 ◽  
Vol 34 (06) ◽  
pp. 1750036
Author(s):  
Lotfi Tadj
Keyword(s):  
Markov Chain ◽  
Steady State ◽  
Queueing System ◽  
System Size ◽  
Embedded Markov Chain ◽  
Queueing Models ◽  
Single Server ◽  
Multiple Vacations ◽  
Service Completion

This paper contributes to the literature of single server queueing models with a vacationing server. We have incorporated many features for a better control over the system. The server implements the N-policy, takes both single and multiple vacations, and is subject to breakdowns. The embedded Markov chain technique is used to obtain the pgf of the system size at a service completion epoch in the steady-state. The semi-regenerative technique is used to obtain the pgf of the system size at an arbitrary instant of time in the steady-state.

On the single-server queue with the preemptive-resume last-come–first-served queue discipline

1986 ◽  
Vol 23 (1) ◽  
pp. 243-248 ◽  
Author(s):  
D. Fakinos
Keyword(s):  
Equilibrium Distribution ◽  
Queueing System ◽  
Independent Random Variables ◽  
Single Server ◽  
Queue Size ◽  
Single Server Queue ◽  
Idle Period ◽  
Preemptive Resume ◽  
Server Queue ◽  
Queue Discipline

The paper considers the GI/G/1 queueing system under the assumption of a last-come–first-served queue discipline, where each customer begins service immediately upon his arrival. At the next arrival, the previous service is interrupted but no loss of service is involved. It has been shown that when the system is considered exclusively at arrival epochs or exclusively at departure epochs, then the equilibrium distribution of the queue-size is geometric, while the remaining durations of the corresponding services are independent random variables each one distributed as the idle period in the dual (inverse) queue. In this paper alternative simpler proofs of the above results are given.

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 Sojourn Times in A Queueing System with Breakdowns and General Retrial Times

Mathematics ◽  
2021 ◽  
Vol 9 (22) ◽  
pp. 2882
Author(s):  
Ivan Atencia ◽  
José Luis Galán-García
Keyword(s):  
Steady State ◽  
Discrete Time ◽  
Queueing System ◽  
Retrial Queue ◽  
Stochastic Decomposition ◽  
Discrete Time System ◽  
Main Research ◽  
Extensive Analysis ◽  
Complete Study ◽  
Number Of Customers

This paper centers on a discrete-time retrial queue where the server experiences breakdowns and repairs when arriving customers may opt to follow a discipline of a last-come, first-served (LCFS)-type or to join the orbit. We focused on the extensive analysis of the system, and we obtained the stationary distributions of the number of customers in the orbit and in the system by applying the generation function (GF). We provide the stochastic decomposition law and the application bounds for the proximity between the steady-state distributions for the queueing system under consideration and its corresponding standard system. We developed recursive formulae aimed at the calculation of the steady-state of the orbit and the system. We proved that our discrete-time system approximates M/G/1 with breakdowns and repairs. We analyzed the busy period of an auxiliary system, the objective of which was to study the customer’s delay. The stationary distribution of a customer’s sojourn in the orbit and in the system was the object of a thorough and complete study. Finally, we provide numerical examples that outline the effect of the parameters on several performance characteristics and a conclusions section resuming the main research contributions of the paper.

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