A two-sided bound for the renewal function when the interarrival distribution is IMRL

Losidis, Sotirios; Politis, Konstadinos

doi:10.1016/j.spl.2017.01.028

Cited by 15 publications

(2 citation statements)

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“…Remark 7 (Little's law revisited). Expression (20) gives an interesting interpretation in a queueing context. Let us suppose here (without loss of generality) that X i = 1 (i.e.…”

Section: General Results: Convergence Of Joint Moments and Distributionmentioning

confidence: 99%

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On a multivariate renewal-reward process involving time delays and discounting: applications to IBNR processes and infinite server queues

Woo

2018

Queueing Syst

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This paper considers a particular renewal-reward process with multivariate discounted rewards (inputs) where the arrival epochs are adjusted by adding some random delays. Then this accumulated reward can be regarded as multivariate discounted Incurred But Not Reported (IBNR) claims in actuarial science and some important quantities studied in queueing theory such as the number of customers in G/G/∞ queues with correlated batch arrivals. We study the long-term behavior of this process as well as its moments. Asymptotic expressions and bounds for the quantities of our interest, and also convergence result for the distribution of this process after renormalization, are studied, when interarrival times and time delays are light tailed. Next, assuming exponentially distributed delays, we derive some explicit and numerically feasible expressions for the limiting joint moments. In such case, for an infinite server queue with renewal arrival process, we obtain limiting results on the expectation of the workload, and the covariance of queue size and workload. Finally, some queueing theoretic applications are provided.AMS 2000 subject classifications: Primary 60G50, 60K30, 62P05, 60K25.

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“…Remark 7 (Little's law revisited). Expression (20) gives an interesting interpretation in a queueing context. Let us suppose here (without loss of generality) that X i = 1 (i.e.…”

Section: General Results: Convergence Of Joint Moments and Distributionmentioning

confidence: 99%

“…as given in (20), Corollary 6. From [7], we use the result of higher order expansions for the function v(x) which is related to the renewal function as…”

Section: High Order Expansionsmentioning

confidence: 86%