1,329 research outputs found
Transient laws of non-stationary queueing systems and their applications
Cover title.Includes bibliographical references (p. 37-39).Supported in part by a Presidential Young Investigator Award, with matching funds from Draper Laboratory. DDM-9158118D. Bertsimas and G. Mourtizinou
Transient laws of non-stationary queueing systems and their applications
Cover title.Includes bibliographical references (p. 37-39).Supported in part by a Presidential Young Investigator Award, with matching funds from Draper Laboratory. DDM-9158118D. Bertsimas and G. Mourtizinou
Combined analysis of transient delay characteristics and delay autocorrelation function in the Geo(X)/G/1 queue
We perform a discrete-time analysis of customer delay in a buffer with batch arrivals. The delay of the kth customer that enters the FIFO buffer is characterized under the assumption that the numbers of arrivals per slot are independent and identically distributed. By using supplementary variables and generating functions, z-transforms of the transient delays are calculated. Numerical inversion of these transforms lead to results for the moments of the delay of the kth customer. For computational reasons k cannot be too large. Therefore, these numerical inversion results are complemented by explicit analytic expressions for the asymptotics for large k. We further show how the results allow us to characterize jitter-related variables, such as the autocorrelation of the delay in steady state
Analysis of the transient delay in a discrete-time buffer with batch arrivals
We perform a discrete-time analysis of the delay of customers in a FIFO buffer with batch arrivals. The numbers of arrivals per slot are independent and identically distributed variables. Since the arrivals come in batches, the delays of the subsequent customers do not constitute a Markov chain, which complicates the analysis. By using generating functions and the supplementary variable technique, moments of the delay of the k-th customer are calculated
Analysis of Markov-modulated infinite-server queues in the central-limit regime
This paper focuses on an infinite-server queue modulated by an independently
evolving finite-state Markovian background process, with transition rate matrix
. Both arrival rates and service rates are depending
on the state of the background process. The main contribution concerns the
derivation of central limit theorems for the number of customers in the system
at time , in the asymptotic regime in which the arrival rates
are scaled by a factor , and the transition rates by a
factor , with . The specific value of
has a crucial impact on the result: (i) for the system
essentially behaves as an M/M/ queue, and in the central limit theorem
the centered process has to be normalized by ; (ii) for ,
the centered process has to be normalized by , with the
deviation matrix appearing in the expression for the variance
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