scholarly journals Stein’s method for the single server queue in heavy traffic

2020 ◽  
Vol 156 ◽  
pp. 108566 ◽  
Author(s):  
Robert E. Gaunt ◽  
Neil Walton
Keyword(s):  
Heavy Traffic ◽  
Stein’S Method ◽  
Single Server ◽  
Stein's Method ◽  
Single Server Queue ◽  
Server Queue

Approximations for delays using asymptotic estimates

1984 ◽  
Vol 16 (01) ◽  
pp. 6
Author(s):  
David Y. Burman ◽  
Donald R. Smith
Keyword(s):  
Markov Process ◽  
Poisson Process ◽  
Heavy Traffic ◽  
Single Server ◽  
Asymptotic Estimates ◽  
Single Server Queue ◽  
Average Delay ◽  
Multiserver Queues ◽  
Server Queue

Consider a general single-server queue where the customers arrive according to a Poisson process whose rate is modulated according to an independent Markov process. The authors have previously reported on limits for the average delay in light and heavy traffic. In this paper we review these results, extend them to multiserver queues, and describe some approximations obtained from them for general delays.

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.

On queues in discrete regenerative environments, with application to the second of two queues in series

1979 ◽  
Vol 11 (04) ◽  
pp. 851-869 ◽  
Author(s):  
K. Balagopal
Keyword(s):  
Limit Theorems ◽  
Heavy Traffic ◽  
Single Server ◽  
Single Server Queue ◽  
Light Traffic ◽  
Queuing Model ◽  
Heavy Traffic Limit ◽  
Server Queue ◽  
In Series ◽  
Queues In Series

Let Un be the time between the nth and (n + 1)th arrivals to a single-server queuing system, and Vn the nth arrival's service time. There are quite a few models in which {Un, Vn , n ≥ 1} is a regenerative sequence. In this paper, some light and heavy traffic limit theorems are proved solely under this assumption; some of the light traffic results, and all the heavy traffic results, are new for two such models treated earlier by the author; and all the results are new for the semi-Markov queuing model. In the last three sections, the results are applied to a single-server queue whose input is the output of a G/G/1 queue functioning in light traffic.

Approximations for delays using asymptotic estimates

1984 ◽  
Vol 16 (1) ◽  
pp. 6-6
Author(s):  
David Y. Burman ◽  
Donald R. Smith
Keyword(s):  
Markov Process ◽  
Poisson Process ◽  
Heavy Traffic ◽  
Single Server ◽  
Asymptotic Estimates ◽  
Single Server Queue ◽  
Average Delay ◽  
Multiserver Queues ◽  
Server Queue

Consider a general single-server queue where the customers arrive according to a Poisson process whose rate is modulated according to an independent Markov process. The authors have previously reported on limits for the average delay in light and heavy traffic. In this paper we review these results, extend them to multiserver queues, and describe some approximations obtained from them for general delays.

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