Discrete-time analysis ofMAP/PH/1 multiclass general preemptive priority queue

2003 ◽  
Vol 50 (6) ◽  
pp. 662-682 ◽  
Author(s):  
Attahiru Sule Alfa ◽  
Bin Liu ◽  
Qi-Ming He
Keyword(s):  
Discrete Time ◽  
Priority Queue ◽  
Time Analysis ◽  
Preemptive Priority

scholarly journals From Exhaustive Vacation Queues to Preemptive Priority Queues with General Interarrival Times

2018 ◽  
Vol 28 (4) ◽  
pp. 695-704
Author(s):  
Dieter Fiems ◽  
Stijn De Vuyst
Keyword(s):  
Discrete Time ◽  
Queueing System ◽  
Queueing Systems ◽  
Probability Generating Function ◽  
Priority Queue ◽  
Preemptive Priority ◽  
Numerical Examples ◽  
Preemptive Resume ◽  
Completion Times ◽  
Priority Queueing

Abstract We consider the discrete-time G/GI/1 queueing system with multiple exhaustive vacations. By a transform approach, we obtain an expression for the probability generating function of the waiting time of customers in such a system. We then show that the results can be used to assess the performance of G/GI/1 queueing systems with server breakdowns as well as that of the low-priority queue of a preemptive MX+G/GI/1 priority queueing system. By calculating service completion times of low-priority customers, various preemptive breakdown/priority disciplines can be studied, including preemptive resume and preemptive repeat, as well as their combinations. We illustrate our approach with some numerical examples.

scholarly journals Time-dependent performance analysis of a discrete-time priority queue

2008 ◽  
Vol 65 (9) ◽  
pp. 641-652 ◽  
Author(s):  
Joris Walraevens ◽  
Dieter Fiems ◽  
Herwig Bruneel
Keyword(s):  
Performance Analysis ◽  
Discrete Time ◽  
Priority Queue ◽  
Time Dependent

Discrete time analysis of a repairable machine

2002 ◽  
Vol 39 (3) ◽  
pp. 503-516 ◽  
Author(s):  
Attahiru Sule Alfa ◽  
I. T. Castro
Keyword(s):  
Detailed Analysis ◽  
Stationary Distribution ◽  
Discrete Time ◽  
Single Machine ◽  
General Distribution ◽  
Optimal Time ◽  
Time Analysis ◽  
Machine System ◽  
Special Cases

We consider, in discrete time, a single machine system that operates for a period of time represented by a general distribution. This machine is subject to failures during operations and the occurrence of these failures depends on how many times the machine has previously failed. Some failures are repairable and the repair times may or may not depend on the number of times the machine was previously repaired. Repair times also have a general distribution. The operating times of the machine depend on how many times it has failed and was subjected to repairs. Secondly, when the machine experiences a nonrepairable failure, it is replaced by another machine. The replacement machine may be new or a refurbished one. After the Nth failure, the machine is automatically replaced with a new one. We present a detailed analysis of special cases of this system, and we obtain the stationary distribution of the system and the optimal time for replacing the machine with a new one.

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