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Effect of global FCFS and relative load distribution in two-class queues with dedicated servers

Herwig Bruneel (UGent) , Willem Mélange (UGent) , Bart Steyaert (UGent) , Dieter Claeys (UGent) and Joris Walraevens (UGent)
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Abstract
In this paper, we investigate multi-class multi-server queueing systems with global FCFS policy, i.e., where customers requiring different types of service— provided by distinct servers— are accommodated in one common FCFS queue. In such scenarios, customers of one class (i.e., requiring a given type of service) may be hindered by customers of other classes. The purpose of this paper is twofold: to gain (qualitative and quantitative) insight into the impact of (i) the global FCFS policy and (ii) the relative distribution of the load amongst the customer classes, on the system performance. We therefore develop and analyze an appropriate discrete-time queueing model with general independent arrivals, two (independent) customer classes and two class-specific servers.We study the stability of the system and derive the system-content distribution at random slot boundaries; we also obtain mean values of the system content and the customer delay, both globally and for each class individually. We then extensively compare these results with those obtained for an analogous system without global FCFS policy (i.e., with individual queues for the two servers). We demonstrate that global FCFS, as well as the relative distribution of the load over the two customer classes, may have a major impact on the system performance.
Keywords
PERFORMANCE ANALYSIS, MULTICLASS QUEUING-NETWORKS, DELAY ANALYSIS, SYSTEMS, SWITCHES, STABILITY, MODEL, Multi-class queues, Dedicated servers, Global FCFS, Relative load distribution

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Chicago
Bruneel, Herwig, Willem Mélange, Bart Steyaert, Dieter Claeys, and Joris Walraevens. 2013. “Effect of Global FCFS and Relative Load Distribution in Two-class Queues with Dedicated Servers.” 4OR-A QUARTERLY JOURNAL OF OPERATIONS RESEARCH 11 (4): 375–391.
APA
Bruneel, H., Mélange, W., Steyaert, B., Claeys, D., & Walraevens, J. (2013). Effect of global FCFS and relative load distribution in two-class queues with dedicated servers. 4OR-A QUARTERLY JOURNAL OF OPERATIONS RESEARCH, 11(4), 375–391.
Vancouver
1.
Bruneel H, Mélange W, Steyaert B, Claeys D, Walraevens J. Effect of global FCFS and relative load distribution in two-class queues with dedicated servers. 4OR-A QUARTERLY JOURNAL OF OPERATIONS RESEARCH. 2013;11(4):375–91.
MLA
Bruneel, Herwig, Willem Mélange, Bart Steyaert, et al. “Effect of Global FCFS and Relative Load Distribution in Two-class Queues with Dedicated Servers.” 4OR-A QUARTERLY JOURNAL OF OPERATIONS RESEARCH 11.4 (2013): 375–391. Print.
@article{4191251,
  abstract     = {In this paper, we investigate multi-class multi-server queueing systems
with global FCFS policy, i.e., where customers requiring different types of service--- provided by distinct servers--- are accommodated in one common FCFS queue. In such scenarios, customers of one class (i.e., requiring a given type of service) may be hindered by customers of other classes. The purpose of this paper is twofold: to gain (qualitative and quantitative) insight into the impact of (i) the global FCFS policy and (ii) the relative distribution of the load amongst the customer classes, on the system performance. We therefore develop and analyze an appropriate discrete-time queueing model with general independent arrivals, two (independent) customer classes and two class-specific servers.We study the stability of the system and derive the system-content distribution at random slot boundaries; we also obtain mean values of the system content and the customer delay, both globally and for each class individually. We then extensively compare these results with those obtained for an analogous system without global FCFS policy (i.e., with individual queues for the two servers). We demonstrate that global FCFS, as well as the relative distribution of the load over the two customer classes, may have a major impact on the system performance.},
  author       = {Bruneel, Herwig and M{\'e}lange, Willem and Steyaert, Bart and Claeys, Dieter and Walraevens, Joris},
  issn         = {1619-4500},
  journal      = {4OR-A QUARTERLY JOURNAL OF OPERATIONS RESEARCH},
  language     = {eng},
  number       = {4},
  pages        = {375--391},
  title        = {Effect of global FCFS and relative load distribution in two-class queues with dedicated servers},
  url          = {http://dx.doi.org/10.1007/s10288-013-0246-z},
  volume       = {11},
  year         = {2013},
}

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