Consider a two-machine Bernoulli production line defined by all but one of the conventions of Subsection 4.1.1. Specifically, assume that instead of the blocked before service, the following convention is used: Machine m1 is blocked during a time slot if it is up at the beginning of this time slot and the buffer is full at the end of the previous time slot (i.e., the blockage of m1 is independent of the status of m2). We refer to this convention as symmetric blocking since both starvation and blocking conventions are of the same nature - they are defined by the state of the buffer and the status of one machine only. Assume for simplicity that the machines are identical, i.e., p1 = p2 =: p.
a) Draw the state transition diagram of the ergodic Markov chain that describes this system and determine the transition probabilities.
b) Derive the expressions for the stationary probabilities of this Markov chain.
c) Plot these stationary probabilities for p = 0:95 and for p = 0:55, assuming that in both cases N = 5.
d) Derive formulas for PR, WIP, BL1 and ST2 as a function of p and N.