Busy period of a single-server Poisson queueing system with splitting and batch delayed-feedback

2016 ◽  
Vol 8 (2) ◽  
pp. 239
Author(s):  
Aliakbar Montazer Haghighi ◽  
Dimitar P. Mishev
Keyword(s):  
Busy Period ◽  
Queueing System ◽  
Delayed Feedback ◽  
Single Server

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.

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.

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.

Queues with semi-Markovian arrivals

1967 ◽  
Vol 4 (02) ◽  
pp. 365-379 ◽  
Author(s):  
Erhan Çinlar
Keyword(s):  
Distribution Function ◽  
Markov Chain ◽  
Finite Number ◽  
Waiting Time ◽  
Busy Period ◽  
Queueing System ◽  
Interarrival Time ◽  
Single Server ◽  
Queue Size

A queueing system with a single server is considered. There are a finite number of types of customers, and the types of successive arrivals form a Markov chain. Further, the nth interarrival time has a distribution function which may depend on the types of the nth and the n–1th arrivals. The queue size, waiting time, and busy period processes are investigated. Both transient and limiting results are given.

Single-server Poisson queueing system with splitting and delayed-feedback: Part I

2011 ◽  
Vol 3 (1) ◽  
pp. 1 ◽  
Author(s):  
Aliakbar Montazer Haghighi ◽  
Stefanka S. Chukova ◽  
Dimitar P. Mishev
Keyword(s):  
Queueing System ◽  
Delayed Feedback ◽  
Single Server

The generalised state-dependent queue: the busy period Erlangian

1974 ◽  
Vol 11 (03) ◽  
pp. 618-623
Author(s):  
B. W. Conolly
Keyword(s):  
Laplace Transform ◽  
Generating Function ◽  
Busy Period ◽  
Continued Fraction ◽  
Queueing System ◽  
Joint Probability ◽  
Single Server ◽  
System State ◽  
State Dependent ◽  
The Laplace Transform

A continued fraction representation is presented of the Laplace transform of the generating function of the fundamental joint probability and density of busy period length measured in customers served and duration in time. The setting is the single server Erlang queueing system where the parameters of negative exponentially distributed arrival and service times have a general dependence on instantaneous system state.

On the busy period in the queueing system GI/G/1

1961 ◽  
Vol 2 (2) ◽  
pp. 217-228 ◽  
Author(s):  
P. D. Finch
Keyword(s):  
Busy Period ◽  
Queueing System ◽  
Single Server ◽  
Standard Notation ◽  
Number Of Authors

A number of authors have studied busy period problems for particular cases of the general single-server queueing system. For example, using the now standard notation of Kendall [7], GI/M/1 was studied by Conolly [3] and Takacs [18]. Earlier work on M/M/1 includes that of Ledermann and Reuter [8] and Bailey [1]. Kendall [6], Takacs [17], and Prabhu [11] have considered M/G/1.

scholarly journals On Distributions of One Class of Random Sums and their Applications

2020 ◽  
Vol 8 (1) ◽  
pp. 153-164
Author(s):  
Ivan Matsak ◽  
Mikhail Moklyachuk
Keyword(s):  
Distribution Function ◽  
Busy Period ◽  
Queueing System ◽  
Single Server ◽  
Redundant System ◽  
Random Sums ◽  
Sums Of Random Variables ◽  
Geiger Muller Counter ◽  
First Moment ◽  
Event Occurrence

We propose results of the investigation of properties of the random sums of random variables. We consider the case, where the number of summands is the first moment of an event occurrence. An integral equation is presented that determines distributions of random sums. With the help of the obtained results we analyse the distribution function of the time during which the Geiger-Muller counter will not lose any particles, the distribution function of the busy period of a redundant system with renewal, and the distribution function of the sojourn times of a single-server queueing system.

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