scholarly journals A queueing system with a fixed accumulation level, random server capacity and capacity dependent service time

1992 ◽  
Vol 15 (1) ◽  
pp. 189-194 ◽  
Author(s):  
Jewgeni H. Dshalalow ◽  
Lotfi Tadj
Keyword(s):  
Explicit Formula ◽  
Stationary Distribution ◽  
Service Time ◽  
Random Number ◽  
Queueing System ◽  
Time Dependent ◽  
Batch Size ◽  
Single Server ◽  
Variable Size ◽  
Queueing Process

This paper introduces a bulk queueing system with a single server processing groups of customers of a variable size. If upon completion of service the queueing level is at leastrthe server takes a batch of sizerand processes it a random time arbitrarily distributed. If the queueing level is less thanrthe server idles until the queue accumulatesrcustomers in total. Then the server capacity is generated by a random number equals the batch size taken for service which lasts an arbitrarily distributed time dependent on the batch size.The objective of the paper is the stationary distribution of queueing process which is studied via semi-regenerative techniques. An ergodicity criterion for the process is established and an explicit formula for the generating function of the distribution is obtained.

scholarly journals MX/G/1 Vacation Queueing System with Two Types of Repair facilities and Server Timeout

2019 ◽  
Vol 8 (9) ◽  
pp. 2040-2043
Keyword(s):  
Size Distribution ◽  
Exponential Distribution ◽  
Service Time ◽  
Queueing System ◽  
Batch Size ◽  
Single Server ◽  
Poisson Arrivals ◽  
Server Failure ◽  
System Length ◽  
General Service

We consider a single server vacation queue with two types of repair facilities and server timeout. Here customers are in compound Poisson arrivals with general service time and the lifetime of the server follows an exponential distribution. The server find if the system is empty, then he will wait until the time ‘c’. At this time if no one customer arrives into the system, then the server takes vacation otherwise the server commence the service to the arrived customers exhaustively. If the system had broken down immediately, it is sent for repair. Here server failure can be rectified in two case types of repair facilities, case1, as failure happens during customer being served willstays in service facility with a probability of 1-q to complete the remaining service and in case2 it opts for new service also who joins in the head of the queue with probability q. Obtained an expression for the expected system length for different batch size distribution and also numerical results are shown

On a property of a refusals stream

1997 ◽  
Vol 34 (03) ◽  
pp. 800-805 ◽  
Author(s):  
Vyacheslav M. Abramov
Keyword(s):  
Waiting Time ◽  
Service Time ◽  
Busy Period ◽  
Elementary Proof ◽  
Queueing System ◽  
Queueing Systems ◽  
Single Server ◽  
Wide Family

This paper consists of two parts. The first part provides a more elementary proof of the asymptotic theorem of the refusals stream for an M/GI/1/n queueing system discussed in Abramov (1991a). The central property of the refusals stream discussed in the second part of this paper is that, if the expectations of interarrival and service time of an M/GI/1/n queueing system are equal to each other, then the expectation of the number of refusals during a busy period is equal to 1. This property is extended for a wide family of single-server queueing systems with refusals including, for example, queueing systems with bounded waiting time.

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 Complete analysis of a discrete-time batch service queue with batch-size-dependent service time under correlated arrival process: D-$MAP/G_n^{(a,b)}/1$

2021 ◽  
Author(s):  
Umesh Chandra Gupta ◽  
Nitin Kumar ◽  
Sourav Pradhan ◽  
Farida Parvez Barbhuiya ◽  
Mohan L Chaudhry
Keyword(s):  
Generating Function ◽  
Discrete Time ◽  
Service Time ◽  
Batch Size ◽  
Arrival Process ◽  
General Distribution ◽  
Complete Analysis ◽  
Service Rate ◽  
Single Server ◽  
Digital Platforms

Discrete-time queueing models find a large number of applications as they are used in modeling queueing systems arising in digital platforms like telecommunication systems and computer networks. In this paper, we analyze an infinite-buffer queueing model with discrete Markovian arrival process. The units on arrival are served in batches by a single server according to the general bulk-service rule, and the service time follows general distribution with service rate depending on the size of the batch being served. We mathematically formulate the model using the supplementary variable technique and obtain the vector generating function at the departure epoch. The generating function is in turn used to extract the joint distribution of queue and server content in terms of the roots of the characteristic equation. Further, we develop the relationship between the distribution at the departure epoch and the distribution at arbitrary, pre-arrival and outside observer's epochs, where the first is used to obtain the latter ones. We evaluate some essential performance measures of the system and also discuss the computing process extensively which is demonstrated by some numerical examples.

On the ordering of tandem queues with exponential servers

1986 ◽  
Vol 23 (01) ◽  
pp. 115-129 ◽  
Author(s):  
Tapani Lehtonen
Keyword(s):  
Service Time ◽  
Queueing System ◽  
Arrival Process ◽  
Single Server ◽  
Tandem Queues ◽  
Departure Process ◽  
Service Stations ◽  
Service Rates

We consider tandem queues which have a general arrival process. The queueing system consists of s (s ≧ 2) single-server service stations and the servers have exponential service-time distributions. Firstly we give a new proof for the fact that the departure process does not depend on the particular allocation of the servers to the stations. Secondly, considering the service rates, we prove that the departure process becomes stochastically faster as the homogeneity of the servers increases in the sense of a given condition. It turns out that, given the sum of the service rates, the departure process is stochastically fastest in the case where the servers are homogeneous.

Monotonicity of the Loss Probabilities of Single Server Finite Queues with Respect to Convex Order of Arrival or Service Processes

1991 ◽  
Vol 5 (1) ◽  
pp. 43-52 ◽  
Author(s):  
Masakiyo Miyazawa ◽  
J. George Shanthikumar
Keyword(s):  
Markov Chain ◽  
Stationary Distribution ◽  
Batch Size ◽  
Service Process ◽  
Single Server ◽  
Finite Markov Chain ◽  
Convex Order ◽  
Finite Queues ◽  
Loss Probabilities

The loss probabilities of customers in the Mx/GI/1/k, GI/Mx/l/k and their related queues such as server vacation models are compared with respect to the convex order of several characteristics, for example, batch size, of the arrival or service process. In the proof, we give a characterization of a truncation expression for a stationary distribution of a finite Markov chain, which is interesting in itself.

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