An M/M/1 Driven Fluid Queue – Continued Fraction Approach

This paper presents complete solutions of the stationary distributions of buffer occupancy and buffer content of a fluid queue driven by an M/M/1 queue. We assume a general boundary condition when compared to the model discussed in Virtamo and Norros [Queueing Systems 16 (1994) 373–386] and Adan and Resing [Queueing Systems 22 (1996) 171–174]. We achieve the required solutions by transforming the underlying system of differential equations using Laplace transforms to a system of difference equations leading to a continued fraction. This continued fraction helps us to find complete solutions. We also obtain the buffer content distribution for this fluid model using the method of Sericola and Tuffin [Queueing Systems 31 (1999) 253–264].

[1]  D. Mitra,et al.  Stochastic theory of a data-handling system with multiple sources , 1982, The Bell System Technical Journal.

[2]  Beatrice Meini,et al.  Solving M/G/1 type Markov chains: recent advances and applications , 1998 .

[3]  Bruno Sericola,et al.  A fluid queue driven by a Markovian queue , 1999, Queueing Syst. Theory Appl..

[4]  P. R. Parthasarathy,et al.  A Computational Approach for Fluid Queues Driven by Truncated Birth–Death Processes , 2000 .

[5]  John P. Lehoczky,et al.  Channels that Cooperatively Service a Data Stream and Voice Messages , 1982, IEEE Trans. Commun..

[6]  E. A. van Doorn,et al.  A fluid queue driven by an infinite-state birth-death process , 1997 .

[7]  Edward G. Coffman,et al.  Controlled stochastic model of a communication system with multiple sources , 1991, IEEE Trans. Inf. Theory.

[8]  Ivo J. B. F. Adan,et al.  Simple analysis of a fluid queue driven by an M/M/1 queue , 1996, Queueing Syst. Theory Appl..

[9]  Thomas E. Stern,et al.  Analysis of separable Markov-modulated rate models for information-handling systems , 1991, Advances in Applied Probability.

[10]  R. B. Lenin,et al.  Fluid queues driven by an M/M/1/N queue , 2000 .

[11]  D. Mitra.  Stochastic theory of a fluid model of producers and consumers coupled by a buffer , 1988, Advances in Applied Probability.

[12]  Jorma T. Virtamo,et al.  Fluid queue driven by anM/M/1 queue , 1994, Queueing Syst. Theory Appl..

[13]  S. Blaabjerg,et al.  Approximating the heterogeneous fluid queue with a birth-death fluid queue , 1995, IEEE Trans. Commun..

[14]  Peter O'Reilly.  Performance Analysis of Data in Burst Switching , 1986, IEEE Trans. Commun..

[15]  Debasis Mitra,et al.  Analysis, approximations and admission control of a multi-service multiplexing system with priorities , 1995, Proceedings of INFOCOM'95.