A new formula for the busy period of a non-empty multiserver queueing system

2003 ◽  
Vol 143 (2-3) ◽  
pp. 401-408 ◽  
Author(s):  
A.M.K. Tarabia
Keyword(s):  
Busy Period ◽  
Queueing System ◽  
New Formula ◽  
Multiserver Queueing System

scholarly journals Analysis of Multiserver Queueing System with Opportunistic Occupation and Reservation of Servers

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Bin Sun ◽  
Moon Ho Lee ◽  
Sergey A. Dudin ◽  
Alexander N. Dudin
Keyword(s):  
System Performance ◽  
Queueing System ◽  
Optimal Choice ◽  
Preemptive Priority ◽  
Rate Dependent ◽  
Service Type ◽  
The Subject ◽  
Multiserver Queueing System

We consider a multiserver queueing system with two input flows. Type-1 customers have preemptive priority and are lost during arrival only if all servers are occupied by type-1 customers. If all servers are occupied, but some provide service to type-2 customers, service of type-2 customer is terminated and type-1 customer occupies the server. If the number of busy servers is less than the thresholdMduring type-2 customer arrival epoch, this customer is accepted. Otherwise, it is lost or becomes a retrial customer. It will retry to obtain service. Type-2 customer whose service is terminated is lost or moves to the pool of retrial customers. The service time is exponentially distributed with the rate dependent on the customer’s type. Such queueing system is suitable for modeling cognitive radio. Type-1 customers are interpreted as requests generated by primary users. Type-2 customers are generated by secondary or cognitive users. The problem of optimal choice of the thresholdMis the subject of this paper. Behavior of the system is described by the multidimensional Markov chain. Its generator, ergodicity condition, and stationary distribution are given. The system performance measures are obtained. The numerical results show the effectiveness of considered admission control.

scholarly journals Single server queues with modified service mechanisms

1962 ◽  
Vol 2 (4) ◽  
pp. 499-507 ◽  
Author(s):  
G. F. Yeo
Keyword(s):  
Time Distribution ◽  
Busy Period ◽  
Queueing System ◽  
Probability Generating Function ◽  
Single Server ◽  
Waiting Time Distribution ◽  
Period Distribution ◽  
Time Dependent Problem ◽  
Stationary Waiting Time ◽  
Special Case

SummaryThis paper considers a generalisation of the queueing system M/G/I, where customers arriving at empty and non-empty queues have different service time distributions. The characteristic function (c.f.) of the stationary waiting time distribution and the probability generating function (p.g.f.) of the queue size are obtained. The busy period distribution is found; the results are generalised to an Erlangian inter-arrival distribution; the time-dependent problem is considered, and finally a special case of server absenteeism is discussed.

scholarly journals M/G/1 vacation model with limited service discipline and hybrid switching-on policy

1997 ◽  
Vol 3 (3) ◽  
pp. 243-253
Author(s):  
Alexander V. Babitsky
Keyword(s):  
Generating Function ◽  
Busy Period ◽  
Optimization Problem ◽  
Queueing System ◽  
Service Discipline ◽  
Multiple Vacations ◽  
Queueing Process ◽  
Vacation Model ◽  
Hybrid Switching ◽  
Limited Service

The author studies an M/G/1 queueing system with multiple vacations. The server is turned off in accordance with the K-limited discipline, and is turned on in accordance with the T-N-hybrid policy. This is to say that the server will begin a vacation from the system if either the queue is empty orKcustomers were served during a busy period. The server idles until it finds at leastNwaiting units upon return from a vacation.Formulas for the distribution generating function and some characteristics of the queueing process are derived. An optimization problem is discussed.

An Uncertain Single-Server Queueing Model

2021 ◽  
pp. 2150001
Author(s):  
Kai Yao
Keyword(s):  
Queueing Theory ◽  
Busy Period ◽  
Queueing System ◽  
Single Server ◽  
Queueing Model ◽  
Uncertainty Distribution ◽  
Uncertain Variables ◽  
Service Efficiency ◽  
Service Times ◽  
Interarrival Times

In the queueing theory, the interarrival times between customers and the service times for customers are usually regarded as random variables. This paper considers human uncertainty in a queueing system, and proposes an uncertain queueing model in which the interarrival times and the service times are regarded as uncertain variables. The busyness index is derived analytically which indicates the service efficiency of a queueing system. Besides, the uncertainty distribution of the busy period is obtained.

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.

On the busy period distribution of the M/G/2 queueing system

1989 ◽  
Vol 26 (04) ◽  
pp. 858-865 ◽  
Author(s):  
Douglas P. Wiens
Keyword(s):  
Linear Combination ◽  
Busy Period ◽  
Queueing System ◽  
Rate Parameter ◽  
Period Distribution ◽  
Special Cases ◽  
Service Times ◽  
Arbitrary Linear Combination

Equations are derived for the distribution of the busy period of the GI/G/2 queue. The equations are analyzed for the M/G/2 queue, assuming that the service times have a density which is an arbitrary linear combination, with respect to both the number of stages and the rate parameter, of Erlang densities. The coefficients may be negative. Special cases and examples are studied.

The Trivariate Distribution of the Maximum Queue Length, the Number of Customers Served and the Duration of the Busy Period for the M/G/1 Queueing System

1969 ◽  
Vol 6 (1) ◽  
pp. 154-161 ◽  
Author(s):  
E.G. Enns
Keyword(s):  
Queue Length ◽  
Busy Period ◽  
Queueing System ◽  
Single Server ◽  
List Type ◽  
Type Number ◽  
Distribution Of The Maximum ◽  
Maximum Queue Length ◽  
Number Of Customers

In the study of the busy period for a single server queueing system, three variables that have been investigated individually or at most in pairs are:1.The duration of the busy period.2.The number of customers served during the busy period.3.The maximum number of customers in the queue during the busy period.

Transient behavior of coverage processes by applications to the infinite-server queue

1993 ◽  
Vol 30 (3) ◽  
pp. 589-601 ◽  
Author(s):  
Sid Browne ◽  
J. Michael Steele
Keyword(s):  
Line Segment ◽  
Busy Period ◽  
Queueing System ◽  
Transient Behavior ◽  
Infinite Server ◽  
Coverage Process ◽  
Server Queue

We obtain the distribution of the length of a clump in a coverage process where the first line segment of a clump has a distribution that differs from the remaining segments of the clump. This result allows us to provide the distribution of the busy period in an M/G/∞ queueing system with exceptional first service, and applications are considered. The result also provides the tool necessary to analyze the transient behavior of an ordinary coverage process, namely the depletion time of the ordinary M/G/∞ system.

Distribution of the busy period in a controllable M/M/2 queue operating under the triadic (0, K, N, M) policy

1990 ◽  
Vol 27 (02) ◽  
pp. 425-432
Author(s):  
Hahn-Kyou Rhee ◽  
B. D. Sivazlian
Keyword(s):  
Steady State ◽  
Busy Period ◽  
Queueing System ◽  
Service Completion ◽  
Special Cases ◽  
Service Stations ◽  
Gambler’S Ruin ◽  
Gambler's Ruin Problem ◽  
Number Of Customers ◽  
System Operating

We consider an M/M/2 queueing system with removable service stations operating under steady-state conditions. We assume that the number of operating service stations can be adjusted at customers' arrival or service completion epochs depending on the number of customers in the system. The objective of this paper is to obtain the distribution of the busy period using the theory of the gambler's ruin problem. As special cases, the distributions of the busy periods for the ordinary M/M/2 queueing system, the M/M/1 queueing system operating under the N policy and the ordinary M/M/1 queueing system are obtained.

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