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Calculation of the GI/G/1 waiting-time distribution and its cumulants from Pollaczek's formulas
12 references·5 citing·35 second hop
Calculation of the GI/G/1 waiting-time distribution and its cumulants from Pollaczek's formulas (1993)Calculation of the GI/G/1 waiting-time di…Solving probability transform functional equations for numerical inversion (1992)Solving probability transform…Asymptotic expansions for waiting time probabilities in an M/G/1 queue with long-tailed service time (1992)Asymptotic expansions for wai…New results on the single server queue with a batch markovian arrival process (1991)New results on the single ser…Applied Probability and Queues (1987)Applied Probability and QueuesComparison Methods for Queues and Other Stochastic Models. (1986)Comparison Methods for Queues…Matrix-Geometric Solutions to Stochastic Models (1984)Matrix-Geometric Solutions to…The Single Server Queue (1983)The Single Server QueueThe queue GI/M/s with customers of different types or the queue GI/Hm/s (1983)The queue GI/M/s with custome…Stochastic Processes in Queueing Theory (1976)Stochastic Processes in Queue…On the algebra of queues (1966)On the algebra of queuesOn Queues in Heavy Traffic (1962)On Queues in Heavy TrafficThe single server queue in heavy traffic (1961)The single server queue in he…MAD Dispersion Measure Makes Extremal Queue Analysis Simple (2022)MAD Dispersion Measure Makes …Load-dependent service queues with application to congestion control in broadband networks (2002)Load-dependent service queues…An overview of Brownian and non-Brownian FCLTs for the single-server queue (2000)An overview of Brownian and n…An operational calculus for probability distributions via Laplace transforms (1996)An operational calculus for p…Maximum Values in Queueing Processes (1995)Maximum Values in Queueing Pr…The Queueing Network Analyzer (1983)A Markov Modulated Characterization of Packetized Voice and Data Traffic and Related Statistical Multiplexer Performance (1986)A single-server queue with server vacations and a class of non-renewal arrival processes (1990)The Markov-modulated Poisson process (MMPP) cookbook (1993)Modeling IP traffic using the batch Markovian arrival process (2003)The theory of queues with a single server (1952)Stochastic Processes Occurring in the Theory of Queues and their Analysis by the Method of the Imbedded Markov Chain (1953)The stability of a queue with non-independent inter-arrival and service times (1962)Fluctuation theory in continuous time (1975)Fluctuation theory in continuous time (1975)Heavy traffic theory for queues with several servers. II (1979)On the theory of queues with many servers (1955)The Queue M|G|1 with Markov Modulated Arrivals and Services (1986)Exponential Approximations for Tail Probabilities in Queues II: Sojourn Time and Workload (1996)On the discounted penalty function in a Markov-dependent risk model (2005)Some Problems in the Theory of Queues (1951)Approximation Methods for Queues with Application to the Fixed-Cycle Traffic Light (1965)Application of the Diffusion Approximation to Queueing Networks I: Equilibrium Queue Distributions (1974)Logarithmic asymptotics for steady-state tail probabilities in a single-server queue (1994)Stochastic theory of a fluid model of producers and consumers coupled by a buffer (1988)Inventory Control in a Fluctuating Demand Environment (1993)To Queue or Not to Queue: Equilibrium Behavior in Queueing Systems (2003)Dynamic server allocation to parallel queues with randomly varying connectivity (1993)Stability, queue length, and delay of deterministic and stochastic queueing networks (1994)Optimal Investment Policies for a Firm With a Random Risk Process: Exponential Utility and Minimizing the Probability of Ruin (1995)Multiple channel queues in heavy traffic. I (1970)Modeling and analysis of manufacturing systems (2016)Stability properties of constrained queueing systems and scheduling policies for maximum throughput in multihop radio networks (1992)Asset Pricing with Heterogeneous Consumers (1996)Manufacturing flow line systems: a review of models and analytical results (1992)The origin of bursts and heavy tails in human dynamics (2005)Modeling bursts and heavy tails in human dynamics (2006)Approximating a Point Process by a Renewal Process, I: Two Basic Methods (1982)Martingale Methods in Financial Modelling (1997)Fluctuations of Lévy Processes with Applications (2014)
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References

  • 1987Applied Probability and Queues2,704 cited
  • 1984Matrix-Geometric Solutions to Stochastic Models1,706 cited
  • 1991New results on the single server queue with a batch markovian arrival process1,085 cited
  • 1986Comparison Methods for Queues and Other Stochastic Models.938 cited
  • 1983The Single Server Queue844 cited
  • 1976Stochastic Processes in Queueing Theory674 cited
  • 1961The single server queue in heavy traffic444 cited
  • 1962On Queues in Heavy Traffic342 cited
  • 1966On the algebra of queues112 cited
  • 1983The queue GI/M/s with customers of different types or the queue GI/Hm/s57 cited
  • 1992Solving probability transform functional equations for numerical inversion55 cited
  • 1992Asymptotic expansions for waiting time probabilities in an M/G/1 queue with long-tailed service time52 cited

Cited by

  • 1996An operational calculus for probability distributions via Laplace transforms46 cited
  • 2002Load-dependent service queues with application to congestion control in broadband networks34 cited
  • 1995Maximum Values in Queueing Processes29 cited

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2000
An overview of Brownian and non-Brownian FCLTs for the single-server queue
21 cited
  • 2022MAD Dispersion Measure Makes Extremal Queue Analysis Simple19 cited