Advanced search
1 file | 602.13 KB

Delay analysis of a two-class batch-service queue with class-dependent variable server capacity

Jens Baetens (UGent) , Bart Steyaert (UGent) , Dieter Claeys (UGent) and Herwig Bruneel (UGent)
Author
Organization
Abstract
In this paper, we analyse the delay of a random customer in a two-class batch-service queueing model with variable server capacity, where all customers are accommodated in a common single-server first-come-first-served queue. The server can only process customers that belong to the same class, so that the size of a batch is determined by the length of a sequence of same-class customers. This type of batch server can be found in telecommunications systems and production environments. We first determine the steady state partial probability generating function of the queue occupancy at customer arrival epochs. Using a spectral decomposition technique, we obtain the steady state probability generating function of the delay of a random customer. We also show that the distribution of the delay of a random customer corresponds to a phase-type distribution. Finally, some numerical examples are given that provide further insight in the impact of asymmetry and variance in the arrival process on the number of customers in the system and the delay of a random customer.
Keywords
Discrete-time, Batch service, Two-class, Variable capacity, BULK-SERVICE, WAFER FABRICATION, ARRIVAL PROCESS, WORK-STATIONS, MODEL, VACATIONS, TIMES, APPROXIMATIONS, PROBABILITIES, PERFORMANCE

Downloads

  • paper.pdf
    • full text
    • |
    • open access
    • |
    • PDF
    • |
    • 602.13 KB

Citation

Please use this url to cite or link to this publication:

Chicago
Baetens, Jens, Bart Steyaert, Dieter Claeys, and Herwig Bruneel. 2018. “Delay Analysis of a Two-class Batch-service Queue with Class-dependent Variable Server Capacity.” Mathematical Methods of Operations Research  88 (1): 37–57.
APA
Baetens, Jens, Steyaert, B., Claeys, D., & Bruneel, H. (2018). Delay analysis of a two-class batch-service queue with class-dependent variable server capacity. MATHEMATICAL METHODS OF OPERATIONS RESEARCH  , 88(1), 37–57.
Vancouver
1.
Baetens J, Steyaert B, Claeys D, Bruneel H. Delay analysis of a two-class batch-service queue with class-dependent variable server capacity. MATHEMATICAL METHODS OF OPERATIONS RESEARCH  . 2018;88(1):37–57.
MLA
Baetens, Jens, Bart Steyaert, Dieter Claeys, et al. “Delay Analysis of a Two-class Batch-service Queue with Class-dependent Variable Server Capacity.” MATHEMATICAL METHODS OF OPERATIONS RESEARCH  88.1 (2018): 37–57. Print.
@article{8544314,
  abstract     = {In this paper, we analyse the delay of a random customer in a two-class batch-service queueing model with variable server capacity, where all customers are accommodated in a common single-server first-come-first-served queue. The server can only process customers that belong to the same class, so that the size of a batch is determined by the length of a sequence of same-class customers. This type of batch server can be found in telecommunications systems and production environments. We first determine the steady state partial probability generating function of the queue occupancy at customer arrival epochs. Using a spectral decomposition technique, we obtain the steady state probability generating function of the delay of a random customer. We also show that the distribution of the delay of a random customer corresponds to a phase-type distribution. Finally, some numerical examples are given that provide further insight in the impact of asymmetry and variance in the arrival process on the number of customers in the system and the delay of a random customer.},
  author       = {Baetens, Jens and Steyaert, Bart and Claeys, Dieter and Bruneel, Herwig},
  issn         = {1432-2994},
  journal      = {MATHEMATICAL METHODS OF OPERATIONS RESEARCH                                },
  keyword      = {Discrete-time,Batch service,Two-class,Variable capacity,BULK-SERVICE,WAFER FABRICATION,ARRIVAL PROCESS,WORK-STATIONS,MODEL,VACATIONS,TIMES,APPROXIMATIONS,PROBABILITIES,PERFORMANCE},
  language     = {eng},
  number       = {1},
  pages        = {37--57},
  title        = {Delay analysis of a two-class batch-service queue with class-dependent variable server capacity},
  url          = {http://dx.doi.org/10.1007/s00186-017-0627-8},
  volume       = {88},
  year         = {2018},
}

Altmetric
View in Altmetric
Web of Science
Times cited: