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Queue Length Distribution in a FIFO Single-Server Queue with Multiple Arrival Streams Having Different Service Time Distributions
14 references·11 citing·34 second hop
Queue Length Distribution in a FIFO Single-Server Queue with Multiple Arrival Streams Having Different Service Time Distributions (2001)Queue Length Distribution in a FIFO Singl…The BMAP/G/1 queue: A tutorial (2005)The BMAP/G/1 queue: A tutorialMatrix-geometric solutions of M/G/1-type Markov chains: a unifying generalized state-space approach (1998)Matrix-geometric solutions of…Markov chains with marked transitions11This research was supported in part by Grant No. DMI-930628 from the National Science Foundation and the K.C. Wang Education Foundation. (1998)Markov chains with marked tra…Queues with marked customers (1996)Queues with marked customersThe workload in theMAP/G/1 queue with state-dependent services:its application to a queue with preemptive resume priority (1994)The workload in theMAP/G/1 qu…Marked point processes as limits of Markovian arrival streams (1993)Marked point processes as lim…Ladder heights and the Markov-modulated M/G/1 queue (1991)Ladder heights and the Markov…A single-server queue with server vacations and a class of non-renewal arrival processes (1990)A single-server queue with se…Stochastic Modeling and the Theory of Queues (1989)Stochastic Modeling and the T…A stable recursion for the steady state vector in markov chains of m/g/1 type (1988)A stable recursion for the st…A distributional form of Little's Law (1988)A distributional form of Litt…The Queue M|G|1 with Markov Modulated Arrivals and Services (1986)The Queue M|G|1 with Markov M…Poisson Arrivals See Time Averages (1982)Poisson Arrivals See Time Ave…The stability of a queue with non-independent inter-arrival and service times (1962)The stability of a queue with…First-come-first-served queues with multiple servers and customer classes (2018)First-come-first-served queue…Fitting correlated arrival and service times and related queueing performance (2017)Fitting correlated arrival an…Applications in Queueing Theory (2013)Applications in Queueing Theo…Analysis of a continuous time SM[K]/PH[K]/1/FCFS queue: Age process, sojourn times, and queue lengths (2012)Analysis of a continuous time…Single-Server Queues with Markov-Modulated Arrivals and Service Speed (2005)Single-Server Queues with Mar…Age Process, Workload Process, Sojourn Times, and Waiting Times in a Discrete Time SM[K]/PH[K]/1/FCFS Queue (2005)Age Process, Workload Process…The Waiting Time Distribution of a TypekCustomer in a Discrete-Time MMAP[K]/PH[K]/c (c = 1, 2) Queue Using QBDs (2004)The Waiting Time Distribution…A simple eigenvalue method for low-order D-BMAP/G/1 queues (2004)A simple eigenvalue method fo…The M/G/1 FIFO Queue with Several Customer Classes (2003)The M/G/1 FIFO Queue with Sev…The delay distribution of a type k customer in a first-come-first-served MMAP[K]/PH[K]/1 queue (2002)The delay distribution of a t…Distributional Form of Little's Law for FIFO Queues with Multiple Markovian Arrival Streams and Its Application to Queues with Vacations (2001)Distributional Form of Little…A Markov Modulated Characterization of Packetized Voice and Data Traffic and Related Statistical Multiplexer Performance (1986)New results on the single server queue with a batch markovian arrival process (1991)Structured Stochastic Matrices of M/G/1 Type and Their Applications. (1991)Tail probabilities with statistical multiplexing and effective bandwidths in multi-class queues (1993)An EM Algorithm for Batch Markovian Arrival Processes and its Comparison to a Simpler Estimation Procedure (2002)Markovian arrivals in stochastic modelling: a survey and some new results (2010)Applied Probability and Queues (1987)Applied Probability and Queues (2003)Multi-server retrial queue with negative customers and disasters (2007)Multi-class Markovian arrival processes and their parameter fitting (2010)Comparison Methods for Queues and Other Stochastic Models (1984)Comparison Methods for Queues and Other Stochastic Models. (1986)The transient BMAP/G/l queue (1994)Structural results for the control of queueing systems using event-based dynamic programming (1998)The N/G/1 queue and its detailed analysis (1980)The Batch Markovian Arrival Process: A Review and Future Work (2001)Multi-dimensional asymptotically quasi-Toeplitz Markov chains and their application in queueing theory (2006)Stochastic Processes Occurring in the Theory of Queues and their Analysis by the Method of the Imbedded Markov Chain (1953)A Proof for the Queuing Formula: L = λ W (1961)Dynamic priority allocation via restless bandit marginal productivity indices (2007)A queue with working breakdowns (2012)Exact analysis of the M/M/k/setup class of Markov chains via recursive renewal reward (2013)Queueing systems with vacations ? A survey (1986)Traffic modeling for telecommunications networks (1994)The theory of queues with a single server (1952)Queueing system MAP|PH|N|N+R with impatient heterogeneous customers as a model of call center (2012)Queueing systems with correlated arrival flows and their applications to modeling telecommunication networks (2017)On Queues in Heavy Traffic (1962)On the stability of interacting queues in a multiple-access system (1988)Stability, queue length, and delay of deterministic and stochastic queueing networks (1994)Telephone Call Centers: Tutorial, Review, and Research Prospects (2003)Feature Article: Optimization for simulation: Theory vs. Practice (2002)Statistical Analysis of a Telephone Call Center (2005)Simulation modeling for analysis (2010)
this work references cited by second hop

References

  • 1989Stochastic Modeling and the Theory of Queues1,605 cited
  • 1982Poisson Arrivals See Time Averages1,220 cited
  • 1962The stability of a queue with non-independent inter-arrival and service times1,045 cited
  • 1990A single-server queue with server vacations and a class of non-renewal arrival processes535 cited
  • 1988A stable recursion for the steady state vector in markov chains of m/g/1 type285 cited
  • 1993Marked point processes as limits of Markovian arrival streams234 cited
  • 2005The BMAP/G/1 queue: A tutorial199 cited
  • 1998Markov chains with marked transitions11This research was supported in part by Grant No. DMI-930628 from the National Science Foundation and the K.C. Wang Education Foundation.129 cited
  • 1996Queues with marked customers119 cited
  • 1988A distributional form of Little's Law89 cited
  • 1994The workload in theMAP/G/1 queue with state-dependent services:its application to a queue with preemptive resume priority78 cited
  • 1986The Queue M|G|1 with Markov Modulated Arrivals and Services53 cited
  • 1991Ladder heights and the Markov-modulated M/G/1 queue52 cited
  • 1998Matrix-geometric solutions of M/G/1-type Markov chains: a unifying generalized state-space approach45 cited

Cited by

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  • 2005Single-Server Queues with Markov-Modulated Arrivals and Service Speed26 cited
  • 2013Applications in Queueing Theory26 cited
  • 2001Distributional Form of Little's Law for FIFO Queues with Multiple Markovian Arrival Streams and Its Application to Queues with Vacations25 cited
  • 2017Fitting correlated arrival and service times and related queueing performance24 cited
  • 2002The delay distribution of a type k customer in a first-come-first-served MMAP[K]/PH[K]/1 queue20 cited
  • 2004The Waiting Time Distribution of a TypekCustomer in a Discrete-Time MMAP[K]/PH[K]/c (c = 1, 2) Queue Using QBDs20 cited
  • 2004A simple eigenvalue method for low-order D-BMAP/G/1 queues19 cited
  • 2005Age Process, Workload Process, Sojourn Times, and Waiting Times in a Discrete Time SM[K]/PH[K]/1/FCFS Queue19 cited
  • 2012Analysis of a continuous time SM[K]/PH[K]/1/FCFS queue: Age process, sojourn times, and queue lengths17 cited
  • 2018First-come-first-served queues with multiple servers and customer classes17 cited
  • 2003The M/G/1 FIFO Queue with Several Customer Classes17 cited