Queuing Theory - M/M/1 queue with priority discipline

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Suppose there is M/M/1 queue with two priority classes implemented. What will happen if either customers of high or low priority class are present ( i.e. customers from only one priority class are present)? Two dimensional Markov chain becomes "effective one dimensional Markov chain"? Will it act as if with FCFS discipline? what is the after-effect on the average wait time for the whole system and both priority class customers?

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