scholarly journals Letter to the Editor—Some Comments on Sven Erlander's Paper: The Remaining Busy Period for a Single Server Queue with Poisson Input

1967 ◽  
Vol 15 (2) ◽  
pp. 357-358
Author(s):  
N. U. Prabhu
Keyword(s):  
Busy Period ◽  
Single Server ◽  
Single Server Queue ◽  
Poisson Input ◽  
Letter To The Editor ◽  
Server Queue

Some perturbation results for the single-server queue with Poisson input

1965 ◽  
Vol 2 (2) ◽  
pp. 462-466 ◽  
Author(s):  
A. M. Hasofer
Keyword(s):  
Service Time ◽  
Single Server ◽  
Single Server Queue ◽  
Poisson Input ◽  
Server Queue ◽  
Image Position ◽  
General Service

In a previous paper [2] the author has studied the single-server queue with non-homogeneous Poisson input and general service time, with particular emphasis on the case when the parameter of the Poisson input is of the form

The number of departures from a semi-Markov queue

1974 ◽  
Vol 11 (04) ◽  
pp. 825-828 ◽  
Author(s):  
D. C. McNickle
Keyword(s):  
Busy Period ◽  
Single Server ◽  
Single Server Queue ◽  
Server Queue ◽  
Customer Type ◽  
Interarrival Times ◽  
Busy Cycle

In this note an identity due to Arjas (1972) is used to express the distribution of the number of departures from a single server queue in which both service and interarrival times may depend on customer type in terms of the busy period and busy cycle processes.

On the integral of the workload process of the single server queue

2003 ◽  
Vol 40 (01) ◽  
pp. 200-225 ◽  
Author(s):  
A. A. Borovkov ◽  
O. J. Boxma ◽  
Z. Palmowski
Keyword(s):  
Service Time ◽  
Time Distribution ◽  
Busy Period ◽  
Single Server ◽  
Service Time Distribution ◽  
Whittaker Functions ◽  
Single Server Queue ◽  
Stieltjes Transform ◽  
Server Queue ◽  
Sequential Approximation

This paper is devoted to a study of the integral of the workload process of the single server queue, in particular during one busy period. Firstly, we find asymptotics of the area 𝒜 swept under the workload process W(t) during the busy period when the service time distribution has a regularly varying tail. We also investigate the case of a light-tailed service time distribution. Secondly, we consider the problem of obtaining an explicit expression for the distribution of 𝒜. In the general GI/G/1 case, we use a sequential approximation to find the Laplace—Stieltjes transform of 𝒜. In the M/M/1 case, this transform is obtained explicitly in terms of Whittaker functions. Thirdly, we consider moments of 𝒜 in the GI/G/1 queue. Finally, we show asymptotic normality of .

Waiting time and workload in queues with periodic Poisson input

1989 ◽  
Vol 26 (02) ◽  
pp. 390-397 ◽  
Author(s):  
Austin J. Lemoine
Keyword(s):  
Differential Equation ◽  
Waiting Time ◽  
Arrival Rate ◽  
Time Of Day ◽  
Single Server ◽  
Single Server Queue ◽  
Poisson Input ◽  
Service Distribution ◽  
Server Queue ◽  
General Service

This paper develops moment formulas for asymptotic workload and waiting time in a single-server queue with periodic Poisson input and general service distribution. These formulas involve the corresponding moments of waiting-time (workload) for the M/G/1 system with the same average arrival rate and service distribution. In certain cases, all the terms in the formulas can be computed exactly, including moments of workload at each ‘time of day.' The approach makes use of an asymptotic version of the Takács [12] integro-differential equation, together with representation results of Harrison and Lemoine [3] and Lemoine [6].

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