Class clustering destroys delay differentiation in priority queues

Bruneel, Herwig; Maertens, Tom; Walraevens, Joris

doi:10.1016/j.ejor.2013.12.005

Cited by 1 publication

(2 citation statements)

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“…For instance, we have observed that class clustering may also have substantial effects on the performance of multi-class queues with multiple class-dedicated servers and a global FCFS service discipline [13,15]. Also, in priority queues interclass correlation has been shown to have a possibly major impact on the delay-differentiating capabilities of the priority rule [31,10,11].…”

Section: Discussionmentioning

confidence: 99%

“…In the above expression, t A and t B are given in equation 2, γ is the interclass correlation defined in (3), C (1) and C (1) are derivatives of the pgf C(z) of the service time of an arbitrary customer, ρ is the load of the system calculated from (11), and p A and p B are the probabilities given by the formulas (18). The first term (ρ) in equation 22corresponds to the mean number of customers in service, the other three terms account for the mean queue content, i.e., the mean number of customers that are actually waiting to be served.…”

Section: System Content At Random Slot Boundariesmentioning

confidence: 99%

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Analysis of a two-class single-server discrete-time FCFS queue: the effect of interclass correlation

Bruneel

Maertens

Steyaert

et al. 2018

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In this paper we study a discrete-time queueing system with one server and two classes of customers. Customers enter the system according to a general independent arrival process. The classes of consecutive customers, however, are correlated in a Markovian way. The system uses a "global FCFS" service discipline, i.e., all arriving customers are accommodated in one single FCFS queue, regardless of their classes. The service-time distribution of the customers is general but class-dependent, and therefore, the exact order in which the customers of both classes succeed each other in the arrival stream is important, which is reflected by the complexity of the system content and waiting time analysis presented in this paper. In particular, a detailed waiting time analysis of this kind of multiclass system has not yet been published, and is considered to be one of the main novelties by the authors. In addition to that, a major aim of the paper is to estimate the impact of interclass correlation in the arrival stream on the total number of customers in the system, and the customer delay. The results reveal that the system can exhibit two different classes of stochastic equilibrium: a "strong" equilibrium where both customer classes give rise to stable behavior individually, and a "compensated" equilibrium where one customer type creates overload.

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