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Margolius, Barbara

doi:10.1023/a:1019145927891

Cited by 18 publications

(7 citation statements)

References 55 publications

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“…Estimates concerning the distance between truncated and infinite models for homogeneous BDP are presented in [9]. Some queueing applications of periodic BDP are given in [7].…”

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confidence: 99%

Some universal limits for nonhomogeneous birth and death processes

et al. 2006

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In this paper we consider nonhomogeneous birth and death processes (BDP) with periodic rates. Two important parameters are studied, which are helpful to describe a nonhomogeneous BDP X = X (t), t ≥ 0: the limiting mean value (namely, the mean length of the queue at a given time t) and the double mean (i.e. the mean length of the queue for the whole duration of the BDP). We find conditions of existence of the means and determine bounds for their values, involving also the truncated BDP X N . Finally we present some examples where these bounds are used in order to approximate the double mean.

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“…Estimates concerning the distance between truncated and infinite models for homogeneous BDP are presented in [9]. Some queueing applications of periodic BDP are given in [7].…”

mentioning

confidence: 99%

Some universal limits for nonhomogeneous birth and death processes

et al. 2006

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“…By assuming some state (generally idle) at time 0, Zhang [61] and Margolius [40] figured out the transient distributions of queue length in the single-server and multi-server cases respectively. Zeifman et al [60] approximated the limiting mean value (expected queue length at some given time) of the single-server model with the transient distribution by restricting their difference to some controllable extent.…”

Section: Time-varying Queuesmentioning

confidence: 99%

“…Margolius [40] and Zeifman et al [60]), subscript t implies that the inter-arrival time or service duration's distributions are time dependent. For instance, the notation M t /M t /1 indicates that it is a single-server queue with time-varying Poisson arrival and the service duration is exponential with time varying rate.…”

Section: Notation and Terminologymentioning

confidence: 99%

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Perfect and nearly perfect sampling of work-conserving queues

2015

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We present sampling-based methods to treat work-conserving queueing systems. A variety of models are studied. Besides the First Come First Served (FCFS) queues, many efforts are putted on the accumulating priority queue (APQ), where a customer accumulates priority linearly while waiting. APQs have Poisson arrivals, multi-class customers with corresponding service durations, and single or multiple servers.Perfect sampling is an approach to draw a sample directly from the steady-state distribution of a Markov chain without explicitly solving for it. Statistical inference can be conducted without initialization bias. If an error can be tolerated within some limit, i.e. the total variation distance between the simulated draw and the stationary distribution can be bounded by a specified number, then we get a so called "nearly" perfect sampling.Coupling from the past (CFTP) is one approach to perfect sampling, but it usually requires a bounded state space. One strategy for perfect sampling on unbounded state spaces relies on construction of a reversible dominating process. If only the dominating property is guaranteed, then regenerative method (RM) becomes an alternative choice. In the case where neither the reversibility nor dominance hold, a nearly perfect sampling method will be proposed. It is a variant of dominated CFTP that we call the CFTP Block Absorption (CFTP-BA) method.Time-varying queues with periodic Poisson arrivals are being considered in this thesis. It has been shown that a particular limiting distribution can be obtained for each point in time in the periodic cycle. Because there are no analytical solutions in closed forms, we explore perfect (or nearly perfect) sampling of these systems.

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“…There is a large number of papers in the queueing literature devoted to analysis of state dependent and time dependent queueing systems as M t /M t /1 and M t /M t /c and associated with their Markovian queueing networks (e.g., see [23][24][25][26][27]). An analysis of such queueing system is motivated by a wide spectra of practical problems well-known in the literature.…”

Section: Introductionmentioning

confidence: 99%

On Existence of Limiting Distribution for Time-Nonhomogeneous Countable Markov Process

Abramov

Liptser

2004

Queueing Systems

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Abstract. In this paper, sufficient conditions are given for the existence of limiting distribution of a nonhomogeneous countable Markov chain with time-dependent transition intensity matrix. The method of proof exploits the fact that if the distribution of random process Q = (Q t ) t 0 is absolutely continuous with respect to the distribution of ergodic random processwhere π is the invariant measure of Q • . We apply this result for asymptotic analysis, as t → ∞, of a nonhomogeneous countable Markov chain which shares limiting distribution with an ergodic birth-anddeath process.

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Untitled

Cited by 18 publications

References 55 publications

Some universal limits for nonhomogeneous birth and death processes

Some universal limits for nonhomogeneous birth and death processes

Perfect and nearly perfect sampling of work-conserving queues

On Existence of Limiting Distribution for Time-Nonhomogeneous Countable Markov Process

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