The workload in theMAP/G/1 queue with state-dependent services:its application to a queue with preemptive resume priority

A Packet Switch with a Priority Scheduling Discipline: Performance Analysis

“…All these models have a packet transmission time of a single slot in common. Furthermore, preemptive resume priority queues have been analyzed in Machihara (1995), Takine (1994a) and Walraevens (2004). Machihara (1995) analyzes waiting times when high-priority arrivals are generated according to a MAP process.…”

“…Machihara (1995) analyzes waiting times when high-priority arrivals are generated according to a MAP process. Takine (1994a) studies the waiting times of customers arriving to a queue according to independent MAP pro-cesses. Finally, Walraevens (2000) analyzes system contents and packet delay when service times are geometrically distributed.…”

DUAL FORM OF MARKOV RENEWAL EQUATIONS AND AN APPLICATION TO ASYMPTOTIC ANALYSIS OF A SINGLE-SERVER QUEUE(<Special Issue>the 50th Anniversary of the Operations Research Society of Japan)

“…It is easy from (14) Next, consider the term corresponding to the denominator of (7). Djlferentiating both sides of (14) in Lemma 3.2 and then applying (14) n(e)K(e)r(O) S n(e)r(e)!A(e), e < Oo, by (15) and the equality holds at e = dv, their gradients on bot･h sides are also equal at e = cr. Thus, differentiating both sides, we have d(1/A(e))/del,=.…”

Analysis of a discrete-time preemptive resume priority buffer

“…In [17], the delay of the low-priority customers is analyzed using probability generating functions. 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.…”

“…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.…”