scholarly journals System occupancy in a multiclass batch-service queueing system with limited variable service capacity

2019 ◽  
Vol 293 (1) ◽  
pp. 3-26
Author(s):  
Jens Baetens ◽  
Bart Steyaert ◽  
Dieter Claeys ◽  
Herwig Bruneel
Keyword(s):  
Queueing System ◽  
Batch Service ◽  
Service Capacity

A queueing system with non-recurrent input and batch servicing

1965 ◽  
Vol 2 (02) ◽  
pp. 442-448
Author(s):  
C. Pearce
Keyword(s):  
Distribution Function ◽  
Queueing System ◽  
Arrival Process ◽  
Batch Service ◽  
Service Times

We consider a queueing system in which arrivals occur at times , and after every kth arrival a servicing of k arrivals is begun. We assume that the number of servers is infinite. Initially, at t 0 = 0, the system is empty and the arrival process {tn } is about to start. The batch service times are independently and identically distributed with distribution function No assumption is made about the process {tn }.

A non-exponential queueing system with independent arrivals and batch servicing

1990 ◽  
Vol 27 (02) ◽  
pp. 401-408
Author(s):  
Nico M. Van Dijk ◽  
Eric Smeitink
Keyword(s):  
Queue Length ◽  
Queueing System ◽  
Length Distribution ◽  
Service Systems ◽  
Batch Service ◽  
Repair System ◽  
Theoretical Interest ◽  
Form Expression ◽  
Queue Length Distribution ◽  
Service Times

We study a queueing system with a finite number of input sources. Jobs are individually generated by a source but wait to be served in batches, during which the input of that source is stopped. The service speed of a server depends on the mode of other sources and thus includes interdependencies. The input and service times are allowed to be generally distributed. A classical example is a machine repair system where the machines are subject to shocks causing cumulative damage. A product-form expression is obtained for the steady state joint queue length distribution and shown to be insensitive (i.e. to depend on only mean input and service times). The result is of both practical and theoretical interest as an extension of more standard batch service systems.

Adaptation of the service capacity in a queueing system which is subjected to a change in the arrival rate at unknown epoch

1978 ◽  
Vol 10 (3) ◽  
pp. 666-681 ◽  
Author(s):  
M. Yadin ◽  
S. Zacks
Keyword(s):  
Exponential Distribution ◽  
Queueing System ◽  
Arrival Rate ◽  
Cost Structure ◽  
Service Capacity ◽  
Service Intensity ◽  
Discounted Cost ◽  
Adaptation Policies ◽  
The Cost ◽  
Optimal Adaptation

The paper studies the problem of optimal adaptation of an M/M/1 queueing station, when the arrival rate λ0 of customers shifts at unknown epoch, τ, to a known value, λ1. The service intensity of the system starts at μ0 and can be increased at most N times to μ1 < μ2 < · · · < μN. The cost structure consists of the cost changing μi to μj (i + 1 ≦ j ≦ N); of maintaining service at rate μ (per unit of time) and of holding customers at the station (per unit of time). Adaptation policies are constrained by the fact that μ can be only increased. A Bayes solution is derived, under the prior assumption that τ has an exponential distribution. This solution minimizes the total expected discounted cost for the entire future.

Optimal control of batch service queues

1973 ◽  
Vol 5 (2) ◽  
pp. 340-361 ◽  
Author(s):  
Rajat K. Deb ◽  
Richard F. Serfozo
Keyword(s):  
Decision Process ◽  
Time Horizon ◽  
Optimal Level ◽  
Batch Size ◽  
Batch Service ◽  
Service Capacity ◽  
Infinite Time ◽  
Discounted Cost ◽  
Markov Decision ◽  
Batch Service Queues

A batch service queue is considered where each batch size and its time of service is subject to control. Costs are incurred for serving the customers and for holding them in the system. Viewing the system as a Markov decision process (i.e., dynamic program) with unbounded costs, we show that policies which minimize the expected continuously discounted cost and the expected cost per unit time over an infinite time horizon are of the form: at a review point when x customers are waiting, serve min {x, Q} customers (Q being the, possibly infinite, service capacity) if and only if x exceeds a certain optimal level M. Methods of computing M for both the discounted and average cost contexts are presented.

scholarly journals Discrete-Time Bulk Queueing System with Variable Service Capacity Depending on Previous Service Time

2015 ◽  
Vol 2015 ◽  
pp. 1-6 ◽  
Author(s):  
Yutae Lee
Keyword(s):  
Generating Function ◽  
Discrete Time ◽  
Service Time ◽  
Queue Length ◽  
Queueing System ◽  
Function Technique ◽  
Supplementary Variable ◽  
Service Capacity ◽  
Bulk Service ◽  
Bulk Arrival

This paper considers a discrete-time bulk-arrival bulk-service queueing system with variable service capacity, where the service capacity varies depending on the previous service time. Using the supplementary variable method and the generating function technique, we obtain the queue length distributions at arbitrary slot boundaries and service completion epochs.

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