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a large system is controlled bynbspnnbspidentical computers each computer independently alternates between an
let n1tnbsptgt0 and n2tnbsptgt0 be independent renewal counting processes assume that each has the same cdf fx for
in this problem we show how to calculate the residual life distributionnbspyt as a transient innbspt letnbspmut
this is a very simple exercise designed to clarify confusion about the roles of past present and future in stopping
assume a friend has developed an excellent program for finding the steady-state probabilities for finite-state markov
consider a ferry that carries cars across a river the ferry holds an integer numbernbspknbspof cars and departs the
renewal theory proof that a class is all recurrent or all transient assume that state j in a countable-state markov
consider an irreducible markov chain that is positive recurrent nbsprecall the technique used to find the expected
a markov chain with states 0 1 2nbspnbspnbspjnbsp- 1 wherenbspjnbspis either finite or infinite has transition
let xnnbspnnbspge 1 denote a positive recurrent markov chain having a countable-state space now consider a new
consider the sampled-time approximation to the mm1 queue in figure 65a give the steady-state probabilities for this
anbspgiven that an arrival occurs in the interval ndelta nnbsp 1delta for the sampled-time mm1 model in figure 65 find
anbspuse the birth and death model described in figure 64 to find the steady-state pmf for the number of customers in
consider a markov process for which the embedded markov chain is a birth-death chain with transition
consider the markov processnbsp fornbsp thenbsp mm1nbsp queuenbsp asnbsp given nbspin figure 74a find the steady-state
consider the markov process illustrated below the transitions are labeled by the ratenbspqijnbspat which those
anbspconsider a markov process with the set of states 0 1nbspnbsp in which the transition rates qij between states are
letnbspqii1 2i-1 for allnbspinbspge 0 and letnbspqii-1 2i-1nbsp for allnbspinbspnbspge 1 nbspall other transition
consider the three-state markov process below the number given nbspon edge inbspj isnbspqij the transition rate
a consider an mm1 queueing system with arrival rate lambda service rate mu mu gt lambda assume that the queue is in
a small bookie shop has room for at most two customers potential cus- tomers arrive at a poisson rate of ten customers
this exercise explores a continuous time version of a simple branching processconsider a population of primitive
consider the job sharing computer system illustrated below incom- ing jobs arrive from the left in a poisson stream
consider the following combined queueing system the first queue sys- tem is mm1 with service ratenbspmu1 the second