Departure processes from MAP/PH/1 queues

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[1]  Gabriel R. Bitran,et al.  Analysis of the ΣPhi/Ph/1 Queue , 1994, Oper. Res..

[2]  E. Coddington An Introduction to Ordinary Differential Equations , 1961 .

[3]  Guy Pujolle,et al.  Introduction to queueing networks , 1987 .

[4]  Nigel G. Bean,et al.  The output process of an MMPP/M/1 queue , 1998, Journal of Applied Probability.

[5]  Philip M. Morse,et al.  Stochastic Properties of Waiting Lines , 1955, Oper. Res..

[6]  C. O'Cinneide On non-uniqueness of representations of phase-type distributions , 1989 .

[7]  Nigel G. Bean,et al.  Some asymptotic properties of two-stage tandem networks of PH/PH/1 queues , 1998 .

[8]  R. R. P. Jackson,et al.  Queueing Systems with Phase Type Service , 1954 .

[9]  Marcel F. Neuts,et al.  Structured Stochastic Matrices of M/G/1 Type and Their Applications , 1989 .

[10]  L Bright,et al.  Equilibrium Distributions for Level-Dependent Quasi-Birth-and-Death Processes , 1996 .

[11]  F. R. Gantmakher The Theory of Matrices , 1984 .

[12]  Susan L. Albin,et al.  Approximating a Point Process by a Renewal Process, II: Superposition Arrival Processes to Queues , 1984, Oper. Res..

[13]  David M. Lucantoni,et al.  New results for the single server queue with a batch Markovian arrival process , 1991 .

[14]  George G. O’Brien,et al.  The Solution of Some Queueing Problems , 1954 .

[15]  Tobias Rydén,et al.  On identifiability and order of continuous-time aggregated Markov chains, Markov-modulated Poisson processes, and phase-type distributions , 1996, Journal of Applied Probability.

[16]  P. Burke The Output Process of a Stationary $M/M/s$ Queueing System , 1968 .

[17]  M. Neuts,et al.  A single-server queue with server vacations and a class of non-renewal arrival processes , 1990, Advances in Applied Probability.

[18]  Colm Art O'Cinneide,et al.  Triangular order of triangular phase-type distributions ∗ , 1993 .

[19]  Noel M. Mirasol Letter to the Editor---The Output of an M/G/∞ Queuing System is Poisson , 1963 .

[20]  Latouche Guy,et al.  A note on two matrices occurring in the solution of quasi-birth-and-death processes , 1987 .

[21]  R. Cuninghame-Green,et al.  Applied Linear Algebra , 1979 .

[22]  Vincent Hodgson,et al.  The Single Server Queue. , 1972 .

[23]  Thomas L. Vlach,et al.  THE DEPARTURE PROCESS FROM THE GI/G/1 QUEUE , 1969 .

[24]  Ward Whitt,et al.  Approximating a Point Process by a Renewal Process, I: Two Basic Methods , 1982, Oper. Res..

[25]  W. Whitt Approximations for departure processes and queues in series , 1984 .

[26]  S. Albin On Poisson Approximations for Superposition Arrival Processes in Queues , 1982 .

[27]  Marcel F. Neuts,et al.  Matrix-Geometric Solutions in Stochastic Models , 1981 .

[28]  P. Burke The Output of a Queuing System , 1956 .

[29]  Sheng-Roan Kai,et al.  Approximation for the departure process of a queue in a network , 1986 .

[30]  M. Neuts,et al.  A SINGLE-SERVER QUEUE WITH SERVER VACATIONS AND A CLASS OF NON-RENEWAL ARRIVAL PROCESSES , 1990 .

[31]  C. O'Cinneide Characterization of phase-type distributions , 1990 .

[32]  Jean Walrand,et al.  On the existence of finite-dimensional filters for Markov-modulated traffic , 1994, Journal of Applied Probability.

[33]  Alexander Graham,et al.  Kronecker Products and Matrix Calculus: With Applications , 1981 .

[34]  E. Reich Waiting Times When Queues are in Tandem , 1957 .

[35]  D. Daley The Correlation Structure of the Output Process of Some Single Server Queueing Systems , 1968 .

[36]  J. Ben Atkinson,et al.  An Introduction to Queueing Networks , 1988 .

[37]  Nigel G. Bean,et al.  When is a MAP poisson , 2000 .

[38]  Daniel G. Shimshak A comparison of waiting time approximations in series queueing systems , 1979 .

[39]  Colm Art O'Cinneide,et al.  Phase-type distributions and invariant polytopes , 1991, Advances in Applied Probability.

[40]  K. Meyer The Output of a Queueing System , 1981 .

[41]  Valerie Isham,et al.  Non‐Negative Matrices and Markov Chains , 1983 .

[42]  Christian Commault,et al.  On dual and minimal phase-type representations , 1993 .

[43]  John Richard Fraker Approximate techniques for the analysis of tandem queueing systems , 1971 .

[44]  Nigel G. Bean,et al.  Quasi-reversibility and quasi-birth-and-death processes , 1998 .

[45]  Marcel F. Neuts,et al.  Algorithmic probability - a collection of problems , 1995, Stochastic modeling series.

[46]  Colm Art O'Cinneide,et al.  Phase-Type Distributions and Majorization , 1991 .

[47]  C. Commault,et al.  An invariant of representations of phase-type distributions and some applications , 1996 .

[48]  V. Ramaswami,et al.  An operator analytic approach to product-farm networks , 1996 .

[49]  Attahiru Sule Alfa,et al.  Advances in matrix-analytic methods for stochastic models , 1998 .