Regenerative analysis of a finite buffer fluid queue

We analyze a feedback system consisting of a finite buffer fluid queue and a responsive source. The source alternates between silence periods and active periods. At random epochs of times, the source becomes ready to send a burst of fluid. The length of the bursts (length of the active periods) are independent and identically distributed with some general distribution. The queue employs a threshold discarding policy in the sense that only those bursts at whose commencement epoch (the instant at which the source is ready to send) the workload (i.e., the amount of fluid in the buffer) is less than some preset threshold are accepted. If the burst is rejected then the source backs off from sending. We work within the framework of Poisson counter-driven stochastic differential equations and obtain the moment generating function and hence the probability density function of the stationary workload process. We then comment on the stability of this fluid queue. Our explicit characterizations will further provide useful insights and “engineering” guidelines for better network designing.

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A fluid queue with a finite buffer and subexponential input

Advances in Applied Probability ◽

10.1239/aap/1013540031 ◽

2000 ◽

Vol 32 (1) ◽

pp. 221-243 ◽

Cited By ~ 18

Author(s):

A. P. Zwart

Keyword(s):

Stationary Distribution ◽

Fluid Model ◽

Buffer Size ◽

Finite Buffer ◽

Asymptotic Results ◽

Fluid Queue ◽

Buffer Content ◽

The Mean ◽

Heavy Tailed ◽

Finite Dam

We consider a fluid model similar to that of Kella and Whitt [32], but with a buffer having finite capacity K. The connections between the infinite buffer fluid model and the G/G/1 queue established by Kella and Whitt are extended to the finite buffer case: it is shown that the stationary distribution of the buffer content is related to the stationary distribution of the finite dam. We also derive a number of new results for the latter model. In particular, an asymptotic expansion for the loss fraction is given for the case of subexponential service times. The stationary buffer content distribution of the fluid model is also related to that of the corresponding model with infinite buffer size, by showing that the two corresponding probability measures are proportional on [0,K) if the silence periods are exponentially distributed. These results are applied to obtain large buffer asymptotics for the loss fraction and the mean buffer content when the fluid queue is fed by N On-Off sources with subexponential on-periods. The asymptotic results show a significant influence of heavy-tailed input characteristics on the performance of the fluid queue.

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Occupation times for the finite buffer fluid queue with phase-type ON-times

Operations Research Letters ◽

10.1016/j.orl.2017.10.012 ◽

2018 ◽

Vol 46 (1) ◽

pp. 27-32 ◽

Cited By ~ 2

Author(s):

N.J. Starreveld ◽

R. Bekker ◽

M. Mandjes

Keyword(s):

Finite Buffer ◽

Occupation Times ◽

Fluid Queue ◽

Phase Type

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A fluid queue with a finite buffer and subexponential input

Advances in Applied Probability ◽

10.1017/s000186780000985x ◽

2000 ◽

Vol 32 (01) ◽

pp. 221-243 ◽

Cited By ~ 4

Author(s):

A. P. Zwart

Keyword(s):

Stationary Distribution ◽

Fluid Model ◽

Buffer Size ◽

Finite Buffer ◽

Asymptotic Results ◽

Fluid Queue ◽

Buffer Content ◽

The Mean ◽

Heavy Tailed ◽

Finite Dam

We consider a fluid model similar to that of Kella and Whitt [32], but with a buffer having finite capacity K. The connections between the infinite buffer fluid model and the G/G/1 queue established by Kella and Whitt are extended to the finite buffer case: it is shown that the stationary distribution of the buffer content is related to the stationary distribution of the finite dam. We also derive a number of new results for the latter model. In particular, an asymptotic expansion for the loss fraction is given for the case of subexponential service times. The stationary buffer content distribution of the fluid model is also related to that of the corresponding model with infinite buffer size, by showing that the two corresponding probability measures are proportional on [0,K) if the silence periods are exponentially distributed. These results are applied to obtain large buffer asymptotics for the loss fraction and the mean buffer content when the fluid queue is fed by N On-Off sources with subexponential on-periods. The asymptotic results show a significant influence of heavy-tailed input characteristics on the performance of the fluid queue.

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On the asymptotic relationship between the overflow probability and the loss ratio

Advances in Applied Probability ◽

10.1239/aap/1011994032 ◽

2001 ◽

Vol 33 (4) ◽

pp. 836-863 ◽

Cited By ~ 13

Author(s):

Han S. Kim ◽

Ness B. Shroff

Keyword(s):

Length Distribution ◽

Upper And Lower Bounds ◽

Log P ◽

Buffer System ◽

Finite Buffer ◽

Loss Ratio ◽

Fluid Queue ◽

Queue Length Distribution ◽

Overflow Probability ◽

Asymptotic Relationship

In this paper we study the asymptotic relationship between the loss ratio in a finite buffer system and the overflow probability (the tail of the queue length distribution) in the corresponding infinite buffer system. We model the system by a fluid queue which consists of a server with constant rate c and a fluid input. We provide asymptotic upper and lower bounds on the difference between log P{Q > x} and logPL(x) under different conditions. The conditions for the upper bound are simple and are satisfied by a very large class of input processes. The conditions on the lower bound are more complex but we show that various classes of processes such as Markov modulated and ARMA type Gaussian input processes satisfy them.

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On the asymptotic relationship between the overflow probability and the loss ratio

Advances in Applied Probability ◽

10.1017/s0001867800011228 ◽

2001 ◽

Vol 33 (04) ◽

pp. 836-863 ◽

Cited By ~ 5

Author(s):

Han S. Kim ◽

Ness B. Shroff

Keyword(s):

Length Distribution ◽

Upper And Lower Bounds ◽

Log P ◽

Buffer System ◽

Finite Buffer ◽

Loss Ratio ◽

Fluid Queue ◽

Queue Length Distribution ◽

Overflow Probability ◽

Asymptotic Relationship

In this paper we study the asymptotic relationship between the loss ratio in a finite buffer system and the overflow probability (the tail of the queue length distribution) in the corresponding infinite buffer system. We model the system by a fluid queue which consists of a server with constant rate c and a fluid input. We provide asymptotic upper and lower bounds on the difference between log P{Q > x} and logP L (x) under different conditions. The conditions for the upper bound are simple and are satisfied by a very large class of input processes. The conditions on the lower bound are more complex but we show that various classes of processes such as Markov modulated and ARMA type Gaussian input processes satisfy them.

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