A Packet Switch with a Priority Scheduling Discipline: Performance Analysis

Analysis of a discrete-time preemptive resume priority buffer

“…If we assume S 2 (z) = (1 − β 2 )z 1 − β 2 z , i.e., the special case of geometrical service times for the low-priority class, we obtain the same equation as found in [24], as expected. From the twodimensional pgf U (z 1 , z 2 ), we can easily derive an expression for the pgf of the total system contents at the beginning of an arbitrary slot -denoted by U T (z) -yielding…”

“…As for the system contents, if we assume S 2 (z) = (1 − β 2 )z 1 − β 2 z , i.e., the special case of geometrical service times for the low-priority customers, we obtain the same equation for the pgf of the class-2 delay as found in [24].…”

“…First, as far as the model is concerned, the arrival processes of the different types of customers are not mutually independent. Note that this arrival model was already used in [24] as well. This correlation between the high-and lowpriority arrival process is however ignored in most other papers on priority queues.…”

“…In [6], [9], [12], [15], [19] and [22] discrete-time priority queues with deterministic service times equal to one slot are studied. Furthermore, preemptive resume priority queues have been analyzed in [10], [17], [18], [23] and [24]. Machihara [10] analyzes waiting times when high-priority arrivals are distributed according to a Markovian arrival process.…”

“…Takine and Hasegawa [18] study the waiting times of customers arriving to a queue according to independent Markovian arrival processes. Finally in [23] and [24], we have analyzed the system contents and customer delay when the service times of high-priority customers are geometrically and generally distributed respectively and the service times of low-priority customers are geometrically distributed.…”