scholarly journals Analysis of a bulk arrival N-policy queue with two-service genre, breakdown, delayed repair under bernoulli vacation and repeated service policy.

2021 ◽  
Author(s):  
Anjana Begum ◽  
Gautam Choudhury
Keyword(s):  
Probability Generating Function ◽  
System Size ◽  
Single Server ◽  
Delayed Repair ◽  
Server Queue ◽  
The Mean ◽  
Bulk Arrival ◽  
Linear Cost ◽  
System Characteristics ◽  
Bernoulli Vacation

This article deals with an unreliable bulk arrival single server queue rendering two-heterogeneous optional repeated service (THORS) with delayed repair, under Bernoulli Vacation Schedule (BVS) and N-policy. For this model, the joint distribution of the server's state and queue length are derived under both elapsed and remaining times. Further, probability generating function (PGF) of the queue size distribution along with the mean system size of the model are determined for any arbitrary time point and service completion epoch, besides various pivotal system characteristics. A suitable linear cost structure of the underlying model is developed, and with the help of a difference operator, a locally optimal N-policy at a lower cost is obtained. Finally, numerical experiments have been carried out in support of the theory.

scholarly journals A bulk queueing system under N-policy with bilevel service delay discipline and start-up time

1993 ◽  
Vol 6 (4) ◽  
pp. 359-384 ◽  
Author(s):  
David C. R. Muh
Keyword(s):  
Queue Length ◽  
Queueing System ◽  
Probability Generating Function ◽  
Single Server ◽  
Numerical Examples ◽  
Queueing Process ◽  
Poisson Input ◽  
Service Delay ◽  
Start Up ◽  
Bulk Arrival

The author studies the queueing process in a single-server, bulk arrival and batch service queueing system with a compound Poisson input, bilevel service delay discipline, start-up time, and a fixed accumulation level with control operating policy. It is assumed that when the queue length falls below a predefined level r(≥1), the system, with server capacity R, immediately stops service until the queue length reaches or exceeds the second predefined accumulation level N(≥r). Two cases, with N≤R and N≥R, are studied.The author finds explicitly the probability generating function of the stationary distribution of the queueing process and gives numerical examples.

scholarly journals Performance Characteristics of Discrete-Time Queue With Variant Working Vacations

2020 ◽  
Vol 11 (2) ◽  
pp. 1-21
Author(s):  
P. Vijaya Laxmi ◽  
Rajesh P.
Keyword(s):  
Discrete Time ◽  
Cost Model ◽  
Probability Generating Function ◽  
System Size ◽  
Service Rate ◽  
Single Server ◽  
Working Vacation ◽  
Optimal Service ◽  
Working Vacations ◽  
Vacation Period

This article analyzes an infinite buffer discrete-time single server queueing system with variant working vacations in which customers arrive according to a geometric process. As soon as the system becomes empty, the server takes working vacations. The server will take a maximum number K of working vacations until either he finds at least on customer in the queue or the server has exhaustively taken all the vacations. The service times during regular busy period, working vacation period and vacation times are assumed to be geometrically distributed. The probability generating function of the steady-state probabilities and the closed form expressions of the system size when the server is in different states have been derived. In addition, some other performance measures, their monotonicity with respect to K and a cost model are presented to determine the optimal service rate during working vacation.

An infinite-server queue subject to an extraneous phase process and related models

1981 ◽  
Vol 18 (1) ◽  
pp. 236-244 ◽  
Author(s):  
P. Purdue ◽  
D. Linton
Keyword(s):  
Original System ◽  
Primary System ◽  
Secondary System ◽  
State Behavior ◽  
Infinite Server ◽  
Server Queue ◽  
Secondary Systems ◽  
Stage System ◽  
The Mean ◽  
Bulk Arrival

We consider an infinite-server queueing system in an extraneous environment. Initially it is shown that the systems of interest can be decomposed into a two-stage system. The primary system is an infinite-server queue with many customer types subject to a clearing mechanism. The secondary system is a special type of bulk-arrival, infinite-server queue. We derive results for the primary and secondary systems separately and combine the results to find the mean steady-state behavior of the original system.

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.

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.

scholarly journals On a single-server queue with fixed accumulation level, state dependent service, and semi-Markov modulated input flow

1992 ◽  
Vol 15 (3) ◽  
pp. 593-600 ◽  
Author(s):  
Jewgeni H. Dshalalow ◽  
Gary Russell
Keyword(s):  
Single Server ◽  
Input Stream ◽  
Idle Period ◽  
Queueing Process ◽  
State Dependent ◽  
Special Cases ◽  
Server Queue ◽  
Semi Markov Process ◽  
The Mean ◽  
Markov Modulated

The authors study the queueing process in a single-server queueing system with state dependent service and with the input modulated by a semi-Markov process embedded in the queueing process. It is also assumed that the server capacity isr≥1and that any service act will not begin until the queue accumulates at leastrunits. In this model, therefore, idle periods also depend upon the queue length.The authors establish an ergodicity criterion for the queueing process and evaluate explicitly its stationary distribution and other characteristics of the system, such as the mean service cycle, intensity of the system, intensity of the input stream, distribution of the idle period, and the mean busy period. Various special cases are treated.

An infinite-server queue subject to an extraneous phase process and related models

1981 ◽  
Vol 18 (01) ◽  
pp. 236-244 ◽  
Author(s):  
P. Purdue ◽  
D. Linton
Keyword(s):  
Original System ◽  
Primary System ◽  
Secondary System ◽  
State Behavior ◽  
Infinite Server ◽  
Server Queue ◽  
Secondary Systems ◽  
Stage System ◽  
The Mean ◽  
Bulk Arrival

We consider an infinite-server queueing system in an extraneous environment. Initially it is shown that the systems of interest can be decomposed into a two-stage system. The primary system is an infinite-server queue with many customer types subject to a clearing mechanism. The secondary system is a special type of bulk-arrival, infinite-server queue. We derive results for the primary and secondary systems separately and combine the results to find the mean steady-state behavior of the original system.

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