Analysis of a discrete-time two-class randomly alternating service model with Bernoulli arrivals

Devos, A.; Walraevens, Joris; Fiems, Dieter; Bruneel, Herwig

doi:10.1007/s11134-020-09663-x

Cited by 8 publications

(17 citation statements)

References 14 publications

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“…We thus observe that, in case of Bernoulli arrivals, S h (s) is the product of three LSTs of exponential random variables. This simple expression is completely in accordance with the results obtained in [29]. In [29], we studied the non-work-conserving model under the assumption of (not necessarily symmetric) Bernoulli arrivals.…”

Section: Bernoulli Arrivalssupporting

confidence: 86%

“…This simple expression is completely in accordance with the results obtained in [29]. In [29], we studied the non-work-conserving model under the assumption of (not necessarily symmetric) Bernoulli arrivals. For this particular case of arrivals, we obtained the joint probability distribution of the number of type-1 and type-2 customers, in steady state.…”

Section: Bernoulli Arrivalssupporting

confidence: 86%

“…For this particular case of arrivals, we obtained the joint probability distribution of the number of type-1 and type-2 customers, in steady state. The corresponding joint probability generating function in [29] turned out to be a rational function.…”

Section: Bernoulli Arrivalsmentioning

confidence: 99%

“…Looking at Figure 2, we observe that the correlation coefficient is always negative. It is worth noting that in [29] it has been shown that for the special case of two independent Bernoulli arrival processes, the correlation coefficient is negative for all allowed values of λ. The reason for this negative correlation coefficient is the service policy.…”

Section: Figurementioning

confidence: 99%

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Heavy-Traffic Comparison of a Discrete-Time Generalized Processor Sharing Queue and a Pure Randomly Alternating Service Queue

et al. 2021

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This paper compares two discrete-time single-server queueing models with two queues. In both models, the server is available to a queue with probability 1/2 at each service opportunity. Since obtaining easy-to-evaluate expressions for the joint moments is not feasible, we rely on a heavy-traffic limit approach. The correlation coefficient of the queue-contents is computed via the solution of a two-dimensional functional equation obtained by reducing it to a boundary value problem on a hyperbola. In most server-sharing models, it is assumed that the system is work-conserving in the sense that if one of the queues is empty, a customer of the other queue is served with probability 1. In our second model, we omit this work-conserving rule such that the server can be idle in case of a non-empty queue. Contrary to what we would expect, the resulting heavy-traffic approximations reveal that both models remain different for critically loaded queues.

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Section: Bernoulli Arrivalssupporting

confidence: 86%

Section: Bernoulli Arrivalssupporting

confidence: 86%

Section: Bernoulli Arrivalsmentioning

confidence: 99%

Section: Figurementioning

confidence: 99%

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Heavy-Traffic Comparison of a Discrete-Time Generalized Processor Sharing Queue and a Pure Randomly Alternating Service Queue

et al. 2021

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show abstract

“…More precisely, the invariant measure of this class of two-dimensional random walk can be written as a finite sum of product-form terms. This work is strongly motivated by the nonwork conserving discrete time two-queue system with Bernoulli arrivals that was recently analysed in [27]. For this model, by using the generating function technique and complex analytic arguments, the authors solved the functional equation and derived the stationary joint queue-length distribution as a sum of three product-form terms.…”

Section: Introductionmentioning

confidence: 99%