Fluid Queues Driven by a Birth and Death Process with Alternating Flow Rates
نویسندگان
چکیده
Fluid queue driven by a birth and death process (BDP) with only one negative effective input rate has been considered in the literature. As an alternative, here we consider a fluid queue in which the input is characterized by a BDP with alternating positive and negative flow rates on a finite state space. Also, the BDP has two alternating arrival rates and two alternating service rates. Explicit expression for the distribution function of the buffer occupancy is obtained. The case where the state space is infinite is also discussed. Graphs are presented to visualize the buffer content distribution.
منابع مشابه
Fluid Queues Driven by a Discouraged Arrivals Queue
We consider a fluid queue driven by a discouraged arrivals queue and obtain explicit expressions for the stationary distribution function of the buffer content in terms of confluent hypergeometric functions. We compare it with a fluid queue driven by an infinite server queue. Numerical results are presented to compare the behaviour of the buffer content distributions for both these models. 1. I...
متن کاملAnalysis of birth-death fluid queues
We present a survey of techniques for analysing the performance of a reservoir which receives and releases fluid at rates which are determined by the state of a background birth-death process. The reservoir is assumed to be infinitely large, but the state space of the modulating birth-death process may be finite or infinite.
متن کاملTransient Analysis of a Fluid Queue Driven by a Birth and Death Process Suggested by a Chain Sequence
We analyse the transient behaviour of a fluid queue driven by a birth and death process (BDP) whose birth and death rates are suggested by a chain sequence. For the BDP suggested by a chain sequence, the stationary probabilities do not exist and hence the stationary buffer content distribution for fluid queues driven by such BDP does not exist. However, their transient distribution is obtained ...
متن کاملMany-Server Limits for Periodic Infinite-Server Queues
To better understand (i) the long-run average performance of periodic many-server queues and (ii) the consequence of fitting a stationary birth-and-death (BD) process to a segment of the sample path of the queue-length process from a many-server system, we establish many-server heavy-traffic fluid limits for the periodic Mt/GI/∞ model. These yield relatively simple fluid approximations for both...
متن کاملFluid Flow Models and Queues— A Connection by Stochastic Coupling
We establish in a direct manner that the steady state distribution of Markovian fluid flow models can be obtained from a quasi birth and death queue. This is accomplished through the construction of the processes on a common probability space and the demonstration of a distributional coupling relation between them. The results here provide an interpretation for the quasi-birth-and-death process...
متن کامل