Abstract
The buffer overflow period in a queue with Markovian arrival process (MAP) and general service time distribution is investigated. The results include distribution of the overflow period in transient and stationary regimes and the distribution of the number of cells lost during the overflow interval. All theorems are illustrated via numerical calculations.
Highlights
One of the crucial performance issues of the single-server queue with finite buffer is losses, namely, customers that were not allowed to enter the system due to the buffer overflow
In a time interval, where the number of customers in the system is equal to its capacity, all arrivals are blocked and lost. We call this interval buffer overflow period and it is equivalent to the remaining service time upon reaching a full buffer
A Markov-modulated Poisson process is constructed by varying the arrival rate of the Poisson process according to an m-state continuous time Markov chain
Summary
One of the crucial performance issues of the single-server queue with finite buffer (waiting room) is losses, namely, customers (packets, cells, jobs) that were not allowed to enter the system due to the buffer overflow. This issue is especially important in the analysis of telecommunication networks. In a time interval, where the number of customers in the system is equal to its capacity, all arrivals are blocked and lost We call this interval buffer overflow period and it is equivalent to the remaining service time upon reaching a full buffer. The FEC technique is based on adding redundant packets to the original sequence in order to protect the transmitted data from the loss of
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