scholarly journals Waiting times in discrete-time cyclic-service systems

1988 ◽  
Vol 36 (2) ◽  
pp. 164-170 ◽  
Author(s):  
O.J. Boxma ◽  
W.P. Groenendijk
Keyword(s):  
Discrete Time ◽  
Waiting Times ◽  
Service Systems ◽  
Cyclic Service

scholarly journals Pseudo-conservation laws in cyclic-service systems

1987 ◽  
Vol 24 (4) ◽  
pp. 949-964 ◽  
Author(s):  
O. J. Boxma ◽  
W. P. Groenendijk
Keyword(s):  
Conservation Laws ◽  
Conservation Law ◽  
Waiting Times ◽  
Service Systems ◽  
Stochastic Decomposition ◽  
Single Server ◽  
Weighted Sum ◽  
Cyclic Service ◽  
The Mean

This paper considers single-server, multi-queue systems with cyclic service. Non-zero switch-over times of the server between consecutive queues are assumed. A stochastic decomposition for the amount of work in such systems is obtained. This decomposition allows a short derivation of a ‘pseudo-conservation law' for a weighted sum of the mean waiting times at the various queues. Thus several recently proved conservation laws are generalised and explained.

scholarly journals Pseudo-conservation laws in cyclic-service systems

1987 ◽  
Vol 24 (04) ◽  
pp. 949-964 ◽  
Author(s):  
O. J. Boxma ◽  
W. P. Groenendijk
Keyword(s):  
Conservation Laws ◽  
Conservation Law ◽  
Waiting Times ◽  
Service Systems ◽  
Stochastic Decomposition ◽  
Single Server ◽  
Weighted Sum ◽  
Cyclic Service ◽  
The Mean

This paper considers single-server, multi-queue systems with cyclic service. Non-zero switch-over times of the server between consecutive queues are assumed. A stochastic decomposition for the amount of work in such systems is obtained. This decomposition allows a short derivation of a ‘pseudo-conservation law' for a weighted sum of the mean waiting times at the various queues. Thus several recently proved conservation laws are generalised and explained.

Algorithmic analysis of the BMAP/D/k system in discrete time

2003 ◽  
Vol 35 (4) ◽  
pp. 1131-1152 ◽  
Author(s):  
Attahiru Sule Alfa
Keyword(s):  
Structural Properties ◽  
Customer Service ◽  
Discrete Time ◽  
Queue Length ◽  
Busy Period ◽  
Marginal Distribution ◽  
Waiting Times ◽  
Single Server ◽  
Waiting Time Distribution ◽  
Algorithmic Analysis

We exploit the structural properties of the BMAP/D/k system to carry out its algorithmic analysis. Specifically, we use these properties to develop algorithms for studying the distributions of waiting times in discrete time and the busy period. One of the structural properties used results from considering the system as having customers assigned in a cyclic order—which does not change the waiting-time distribution—and then studying only one arbitrary server. The busy period is defined as the busy period of an arbitrary single server based on this cyclic assignment of customers to servers. Finally, we study the marginal distribution of the joint queue length and phase of customer arrival. The structural property used for studying the queue length is based on the observation of the system every interval that is the length of one customer service time.

scholarly journals Exact Time-Dependent Queue-Length Solution to a Discrete-Time Geo/D/1 Queue

Mathematics ◽  
2019 ◽  
Vol 7 (8) ◽  
pp. 717
Author(s):  
Jung Woo Baek ◽  
Yun Han Bae
Keyword(s):  
Closed Form ◽  
Discrete Time ◽  
Real World ◽  
Queue Length ◽  
Service Systems ◽  
Time Dependent ◽  
World Systems ◽  
Exact Time ◽  
Queuing Models

Time-dependent solutions to queuing models are beneficial for evaluating the performance of real-world systems such as communication, transportation, and service systems. However, restricted results have been reported due to mathematical complexity. In this study, we present a time-dependent queue-length formula for a discrete-time G e o / D / 1 queue starting with a positive number of initial customers. We derive the time-dependent formula in closed form.

Algorithmic analysis of the BMAP/D/k system in discrete time

2003 ◽  
Vol 35 (04) ◽  
pp. 1131-1152
Author(s):  
Attahiru Sule Alfa
Keyword(s):  
Structural Properties ◽  
Customer Service ◽  
Discrete Time ◽  
Queue Length ◽  
Busy Period ◽  
Marginal Distribution ◽  
Waiting Times ◽  
Single Server ◽  
Waiting Time Distribution ◽  
Algorithmic Analysis

We exploit the structural properties of the BMAP/D/k system to carry out its algorithmic analysis. Specifically, we use these properties to develop algorithms for studying the distributions of waiting times in discrete time and the busy period. One of the structural properties used results from considering the system as having customers assigned in a cyclic order—which does not change the waiting-time distribution—and then studying only one arbitrary server. The busy period is defined as the busy period of an arbitrary single server based on this cyclic assignment of customers to servers. Finally, we study the marginal distribution of the joint queue length and phase of customer arrival. The structural property used for studying the queue length is based on the observation of the system every interval that is the length of one customer service time.

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