Stochastic Estimation of On-Time Message Delivery in a Packet-Switched Network with Messages of Different Priorities

We have developed an approach to estimate the message delivery time distribution for a packet-switched network with different priority classes of messages. This approach is based on approximate formulas for residence time in a multichannel priority system. This formula is similar to approximate formula for the average residence time of a fixed priority customer in a multi-channel queuing system with the non-preemptive or preemptive-resume discipline (relative or absolute priorities) and Poisson input. In the case of single-channel system, in the case of a multichannel system where the service time of the application is distributed exponentially with parameter, independent of the request priority, the formulas for preemptive or non-preemptive priority discipline are exact. These formulas are also exact in the case in which the service time of a customer with some probability, dependent on the priority, is zero, and with an additional probability is distributed exponentially with the same for all priorities parameter. The flow intensity for any line and priority class is calculated with summarizing flow intensities on all routes passing through the line. The expectation of the sum of the message transmission and waiting time for each line is calculated by the proposed formula. The dispersion of this sum is calculated under the assumption that the sum is distributed exponentially. The expectation and dispersion of the message delivery time are calculated under the assumption that the distribution of this time is the gamma-distribution with the calculated values of the expectation and dispersion.