Abstract
In this paper, a fluid queue driven by truncated queue with discouraged arrivals is considered. Using the efficient matrix technique, the expressions of the steady-state distribution of both the buffer content and stationary state probabilities of background birth-death process are acquired. Then, performance measures and analysis of server utilization and mean buffer content are carried out.
Highlights
The study of fluid queueing system with finite space is very useful and important in a plethora of modern applications
Closed form expressions of eigenvalues and eigenvectors are obtained by Lenin and Parthasarathy [6] for the tridiagonal matrix in fluid queues driven by an M/M/1/N queue
Mao et al [8, 9] discussed a fluid model driven by a simple queue having single and multiple exponential vacations
Summary
The study of fluid queueing system with finite space is very useful and important in a plethora of modern applications. A system matrix for Laplace transform is derived for the steady-state distribution of the occupancy of buffer, in the “Model description” section, and solve it using the matrix approach method in the “Stationary solution of fluid queue driven by M/M/1/N queue with discouraged arrivals” section Some performance measures, such as mean buffer content and server utilization, are obtained in the “Some performance measures in fluid model” section. Assume that there is a fluid model driven by a single-server queueing process having state-dependent arrival and service rates. The fluid model discussed in the previous section is investigated when it has the background process as an M/M/1/N queue with mean arrival and service rates to be λj λ jþ and μj =.
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