Investigation of Queueing System Suitable for Mathematical Modelling of TCP Short Transfer

A single-server queueing system with stationary Poisson arrival process, finite buffer and impatient customers as a model of TCP Short Transfer is investigated. Service time of a customer by a server has an exponential distribution. If the server is busy and the buffer is full at a customer arrival epoch, the customer may leave the system forever or move to the orbit. Customers staying in the buffer exhibit signs of impatience: they can leave the buffer lying out of the service. Patience time of a customer has an exponential distribution. When this time expires the customer either leaves the system permanently or goes to the orbit of infinite size. Customers staying in the orbit repeat their attempts to get the service later on in a random amount of time. This time is exponentially distributed with the rate depending or independent of the current number of customers in the orbit.

Behavior of the system under study is described by two-dimensional asymptotically quasi-Toeplitz Markov chain. Stability conditions and the algorithms for calculating the stationary state distribution of the chain are obtained. Main performance measures of the system are calculated.