Heavy traffic results for single-server queues with dependent (EARMA) service and interarrival times

1980 ◽  
Vol 12 (2) ◽  
pp. 517-529 ◽  
Author(s):  
Patricia A. Jacobs
Keyword(s):  
Waiting Time ◽  
Heavy Traffic ◽  
Single Server ◽  
Single Server Queue ◽  
Linear Combinations ◽  
Traffic Conditions ◽  
Server Queue ◽  
Exponential Random Variables ◽  
Service Times ◽  
Multivariate Exponential

Models are given for sequences of correlated exponential interarrival and service times for a single-server queue. These multivariate exponential models are formed as probabilistic linear combinations of sequences of independent exponential random variables and are easy to generate on a computer. Limiting results for customer waiting time under heavy traffic conditions are obtained for these queues. Heavy traffic results are useful for analyzing the effect of correlated interarrival and service times in queues on such quantities as queue length and customer waiting time. They can also be used to check simulation results.

Heavy traffic results for single-server queues with dependent (EARMA) service and interarrival times

1980 ◽  
Vol 12 (02) ◽  
pp. 517-529 ◽  
Author(s):  
Patricia A. Jacobs
Keyword(s):  
Waiting Time ◽  
Heavy Traffic ◽  
Single Server ◽  
Single Server Queue ◽  
Linear Combinations ◽  
Traffic Conditions ◽  
Server Queue ◽  
Exponential Random Variables ◽  
Service Times ◽  
Multivariate Exponential

Models are given for sequences of correlated exponential interarrival and service times for a single-server queue. These multivariate exponential models are formed as probabilistic linear combinations of sequences of independent exponential random variables and are easy to generate on a computer. Limiting results for customer waiting time under heavy traffic conditions are obtained for these queues. Heavy traffic results are useful for analyzing the effect of correlated interarrival and service times in queues on such quantities as queue length and customer waiting time. They can also be used to check simulation results.

A single-server queue with limited virtual waiting time

1974 ◽  
Vol 11 (03) ◽  
pp. 612-617 ◽  
Author(s):  
Lajos Takács
Keyword(s):  
Waiting Time ◽  
Single Server ◽  
Single Server Queue ◽  
Limiting Distributions ◽  
Poisson Input ◽  
Virtual Waiting Time ◽  
General Service Times ◽  
Server Queue ◽  
Service Times ◽  
General Service

The limiting distributions of the actual waiting time and the virtual waiting time are determined for a single-server queue with Poisson input and general service times in the case where there are two types of services and no customer can stay in the system longer than an interval of length m.

A single-server queue with limited virtual waiting time

1974 ◽  
Vol 11 (3) ◽  
pp. 612-617 ◽  
Author(s):  
Lajos Takács
Keyword(s):  
Waiting Time ◽  
Single Server ◽  
Single Server Queue ◽  
Limiting Distributions ◽  
Poisson Input ◽  
Virtual Waiting Time ◽  
General Service Times ◽  
Server Queue ◽  
Service Times ◽  
General Service

The limiting distributions of the actual waiting time and the virtual waiting time are determined for a single-server queue with Poisson input and general service times in the case where there are two types of services and no customer can stay in the system longer than an interval of length m.

The single-server queue with service depending on queue size and with the preemptive-resume last-come–first-served queue discipline

1987 ◽  
Vol 24 (03) ◽  
pp. 758-767
Author(s):  
D. Fakinos
Keyword(s):  
Queueing System ◽  
Limiting Distribution ◽  
Single Server ◽  
Queue Size ◽  
Single Server Queue ◽  
Preemptive Resume ◽  
Server Queue ◽  
Queue Discipline ◽  
Service Times

This paper studies theGI/G/1 queueing system assuming that customers have service times depending on the queue size and also that they are served in accordance with the preemptive-resume last-come–first-served queue discipline. Expressions are given for the limiting distribution of the queue size and the remaining durations of the corresponding services, when the system is considered at arrival epochs, at departure epochs and continuously in time. Also these results are applied to some particular cases of the above queueing system.

scholarly journals Single-Server Queue with Markov-Dependent Inter-Arrival and Service Times

2006 ◽  
Vol 54 (1) ◽  
pp. 79-79
Author(s):  
I. J. B. F. Adan ◽  
V. G. Kulkarni
Keyword(s):  
Single Server ◽  
Single Server Queue ◽  
Server Queue ◽  
Service Times

On the single server queue with preemptive service interruptions

1971 ◽  
Vol 8 (4) ◽  
pp. 835-837 ◽  
Author(s):  
İzzet Şahin
Keyword(s):  
Integral Equation ◽  
Waiting Time ◽  
Stochastic System ◽  
Single Server ◽  
Single Server Queue ◽  
Service Interruptions ◽  
Time Problem ◽  
Server Queue ◽  
Waiting Time Problem ◽  
Limiting Behaviour

In [4], the limiting behaviour of a stochastic system with two types of input was investigated by reducing the problem to the solution of an integral equation. In this note we use the same approach to study the equilibrium waiting time problem for the general single server queue with preemptive service interruptions. (For a comprehensive account of the existing literature on queues with service interruptions we refer to [2] and [3].)

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