On the Two-Class M/M/1 System under Preemptive Resume and Impatience of the Prioritized Customers
Please always quote using this URN: urn:nbn:de:0297-zib-6953
- The paper deals with the two-class priority M/M/1 system, where the prioritized class-1 customers are served under FCFS preemptive resume discipline and may become impatient during their waiting for service with generally distributed maximal waiting times but finite expectation. The class-2 customers have no impatience. The required mean service times may depend on the class of the customer. As the dynamics of class-1 customers are related to the well analyzed M/M/1+GI system, our aim is to derive characteristics for class-2 customers and for the whole system. The solution of the balance equations for the partial probability generating functions of the detailed system state process is given in terms of the weak solution of a family of boundary value problems for ordinary differential equations. By means of this solution formulae for the joint occupancy distribution and for the sojourn and waiting times of class-2 customers are derived generalizing results recently obtained by Choi et al. in case of deterministic maximal waiting times. For deterministic maximal waiting times partially new explicit formulae are given.
Author: | Andreas Brandt, Manfred Brandt |
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Document Type: | ZIB-Report |
Tag: | impatient customers; occupancy distribution; preemptive resume; sojourn time; two-class priority M/M/1 system; waiting time |
MSC-Classification: | 60-XX PROBABILITY THEORY AND STOCHASTIC PROCESSES (For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX) / 60Kxx Special processes / 60K25 Queueing theory [See also 68M20, 90B22] |
68-XX COMPUTER SCIENCE (For papers involving machine computations and programs in a specific mathematical area, see Section -04 in that area) / 68Mxx Computer system organization / 68M20 Performance evaluation; queueing; scheduling [See also 60K25, 90Bxx] | |
90-XX OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING / 90Bxx Operations research and management science / 90B22 Queues and service [See also 60K25, 68M20] | |
Date of first Publication: | 2002/07/10 |
Series (Serial Number): | ZIB-Report (02-28) |
ZIB-Reportnumber: | 02-28 |
Published in: | Appeared in: Queuing Systems, 47 (2004) 147-168 |