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• W2486524710 abstract "We consider an infinite-capacity buffer receiving fluid at a rate depending on the state of an M/M/1 queue. We obtain a new analytic expression for the joint stationary distribution of the buffer level and the state of the M/M/1 queue. This expression is obtained by the use of generating functions which are explicitly inverted. The case of a finite capacity fluid queue is also considered. Markov-modulated fluid flow models have turned out to be very useful in analysing per- formance issues in telecommunication systems. These models are composed of a buffer and a continuous-time Markov chain that controls the input and service rates of the fluid in the buffer. In most studies dealing with the analysis of such fluid queues, the state space of the background Markov chain is supposed to be finite; see, for instance, (4), (8) and the references therein. We consider here an infinite-capacity fluid queue where the input rate is a function of the state of the server in an M/M/1 queue and where the service rate is constant. As suggested in (10), this model might represent a Poisson stream of packet arrivals, where the packet length is exponentially distributed. This stream is buffered in a queue and served with a constant rate. The output process of this M/M/1 queue forms the input process of the fluid queue. The stationary behaviour of that fluid queue has been analysed in several papers. Although approaches are different, the fluid level distribution is generally obtained as an integral expres- sion. First, in (10), Virtamo and Norros solved the well-known infinite differential system by studying the continuous spectrum of a key matrix. Secondly, Adan and Resing (1) considered the background process as an alternating renewal process, corresponding to the successive idle and busy periods of the M/M/1 queue. By renewal theory arguments, the fluid level distribution is given in terms of an integral of Bessel functions. They also obtained the expression of Virtamo and Norros via an integral representation of Bessel functions. More general input processes are applied to that fluid model. In (9), van Doorn and Scheinhart studied a fluid queue fed by an infinite-state birth-death process. They solve the infinite differential system by the use of orthogonal polynomials with respect to a signed measure which is given explicitly in the case of the M/M/1 queue and leads to the same integral expression obtained in (10) and (1). In (7), the authors considered a fluid queue driven by a general" @default.
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• W2486524710 date "2002-01-01" @default.
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• W2486524710 title "QUEUE FED BY AN M/M/1 QUEUE" @default.
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