On Switching Problems Requiring Queuing Theory in Computer-Based Systems

Consider
N
terminal sets connected to a "black box" by
N
lines, one from each set. This box has
K \leq N
output lines. This box connects one of the input lines to one of the output lines when so requested and breaks that connection when the terminal has finished transmission. The output lines can be connected to the input lines in many different ways. Each method leads to a different cost and efficiency. As a measure of efficiency, we take the average time that a message, which arrives at random, has to wait before it can be transmitted. Using queuing theory we show that the mean waiting time is the same for any method of services however, the standard deviations differ.