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.

Queues with semi-Markovian arrivals

1967 ◽  
Vol 4 (2) ◽  
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.

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 Priority Queue with Many Customer Types, Correlated Arrivals and Changing Priorities

Mathematics ◽  
2020 ◽  
Vol 8 (8) ◽  
pp. 1292
Author(s):  
Seokjun Lee ◽  
Sergei Dudin ◽  
Olga Dudina ◽  
Chesoong Kim ◽  
Valentina Klimenok
Keyword(s):  
Markov Chain ◽  
Waiting Time ◽  
Performance Indicators ◽  
Queueing System ◽  
Priority Queue ◽  
First Aid ◽  
Single Server ◽  
Finite Buffer ◽  
Impatient Customers ◽  
Arrival Times

A single-server queueing system with a finite buffer, several types of impatient customers, and non-preemptive priorities is analyzed. The initial priority of a customer can increase during its waiting time in the queue. The behavior of the system is described by a multi-dimensional Markov chain. The generator of this chain, having essential dependencies between the components, is derived and formulas for computation of the most important performance indicators of the system are presented. The dependence of some of these indicators on the capacity of the buffer space is illustrated. The profound effect of the phenomenon of correlation of successive inter-arrival times and variance of the service time is numerically demonstrated. Results can be used for the optimization of dispatching various types of customers in information transmission systems, emergency departments and first aid stations, perishable foods supply chains, etc.

A queueing system with Markov-dependent arrivals

1985 ◽  
Vol 22 (03) ◽  
pp. 668-677 ◽  
Author(s):  
Pyke Tin
Keyword(s):  
Special Reference ◽  
Correlation Coefficient ◽  
Waiting Time ◽  
Serial Correlation ◽  
Queueing System ◽  
Arrival Process ◽  
Single Server ◽  
Queue Size ◽  
Interarrival Times ◽  
Serial Correlation Coefficient

This paper considers a single-server queueing system with Markov-dependent interarrival times, with special reference to the serial correlation coefficient of the arrival process. The queue size and waiting-time processes are investigated. Both transient and limiting results are given.

A queueing system with Markov-dependent arrivals

1985 ◽  
Vol 22 (3) ◽  
pp. 668-677 ◽  
Author(s):  
Pyke Tin
Keyword(s):  
Special Reference ◽  
Correlation Coefficient ◽  
Waiting Time ◽  
Serial Correlation ◽  
Queueing System ◽  
Arrival Process ◽  
Single Server ◽  
Queue Size ◽  
Interarrival Times ◽  
Serial Correlation Coefficient

This paper considers a single-server queueing system with Markov-dependent interarrival times, with special reference to the serial correlation coefficient of the arrival process. The queue size and waiting-time processes are investigated. Both transient and limiting results are given.

scholarly journals On Mx/(G1G2)/1/G(BS)/Vs vacation queue with two types of general heterogeneous service

2005 ◽  
Vol 2005 (3) ◽  
pp. 123-135 ◽  
Author(s):  
Kailash C. Madan ◽  
Z. R. Al-Rawi ◽  
Amjad D. Al-Nasser
Keyword(s):  
Steady State ◽  
Performance Measures ◽  
Waiting Time ◽  
Busy Period ◽  
Single Server ◽  
Queue Size ◽  
Single Vacation ◽  
The Mean ◽  
Expected Waiting Time ◽  
Heterogeneous Service

We analyze a batch arrival queue with a single server providing two kinds of general heterogeneous service. Just before his service starts, a customer may choose one of the services and as soon as a service (of any kind) gets completed, the server may take a vacation or may continue staying in the system. The vacation times are assumed to be general and the server vacations are based on Bernoulli schedules under a single vacation policy. We obtain explicit queue size distribution at a random epoch as well as at a departure epoch and also the mean busy period of the server under the steady state. In addition, some important performance measures such as the expected queue size and the expected waiting time of a customer are obtained. Further, some interesting particular cases are also discussed.

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.

Time dependence of queues with semi-Markovian services

1967 ◽  
Vol 4 (02) ◽  
pp. 356-364 ◽  
Author(s):  
Erhan Çinlar
Keyword(s):  
Finite Number ◽  
Time Dependence ◽  
Service Time ◽  
Queueing System ◽  
Single Server ◽  
Queue Size ◽  
Poisson Input

A single server queueing system with Poisson input is considered. There are a finite number of types of customers and the service time of the nth customers depends on the types of the nth and the (n – l)th customers. The time dependence of the queue size process will be studied, (it will be clear how the methods of the paper can be applied to other processes of interest,) and limiting as well as transient results will be given.

scholarly journals Isomorphs of a class of Queueing systems

1979 ◽  
Vol 2 (1) ◽  
pp. 103-110
Author(s):  
A. Ghosal ◽  
Sudhir Madan
Keyword(s):  
Distribution Function ◽  
Waiting Time ◽  
Queueing Systems ◽  
Idle Time ◽  
Single Server ◽  
Queue Size ◽  
Restricted Sense

Restricted isomorphism between two queueing systems implies that they have equivalent distribution function for at least one (but not all) output elements (e.g. waiting time, queue size, idle time, etc.). Quasi-isomorphism implies an approximate equivalence. Most of the single-server queueing systems can be approximated by a quasi-isomorphic system which has a gamma inter-arrival and gamma service distributions(Ep/Eq/1).This paper deals with the derivation of simpler isomorphs (in quasi-restricted sense) for such gamma-gamma(Ep/Eq/1)systems.

Time dependence of queues with semi-Markovian services

1967 ◽  
Vol 4 (2) ◽  
pp. 356-364 ◽  
Author(s):  
Erhan Çinlar
Keyword(s):  
Finite Number ◽  
Time Dependence ◽  
Service Time ◽  
Queueing System ◽  
Single Server ◽  
Queue Size ◽  
Poisson Input

A single server queueing system with Poisson input is considered. There are a finite number of types of customers and the service time of the nth customers depends on the types of the nth and the (n – l)th customers. The time dependence of the queue size process will be studied, (it will be clear how the methods of the paper can be applied to other processes of interest,) and limiting as well as transient results will be given.

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