Mixing
Number of people waiting in a M/G/$infty$ queue at time t
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For a M/G/$infty$ queue (parameter of M is $lambda=1$), we are given that G ~ U(0,3). My goal is to find the probability that there is no one waiting in the queue at time t = 10. So far, I have broken down the problem into two non-homogeneous Poisson processes: $N(t) = W(t) + D(t)$, where W is the number of people waiting and D is the number of people already departed. An incoming customer at time s is classified as D(t) if service time is less than t -s and similarly is classified as W(t) if service time is greater than t-s. This is where I ran into trouble: computing the closed form for $lambda(t)$. Once I have this, I could apply the fact that W(t) is a non-homogeneous Poisson process to easily find $P(W(10)=0)$
probability stochastic-processes poisson-process queueing-theory
asked 2 days ago
jrstevens
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For a M/G/$infty$ queue (parameter of M is $lambda=1$), we are given that G ~ U(0,3). My goal is to find the probability that there is no one waiting in the queue at time t = 10. So far, I have broken down the problem into two non-homogeneous Poisson processes: $N(t) = W(t) + D(t)$, where W is the number of people waiting and D is the number of people already departed. An incoming customer at time s is classified as D(t) if service time is less than t -s and similarly is classified as W(t) if service time is greater than t-s. This is where I ran into trouble: computing the closed form for $lambda(t)$. Once I have this, I could apply the fact that W(t) is a non-homogeneous Poisson process to easily find $P(W(10)=0)$
probability stochastic-processes poisson-process queueing-theory
asked 2 days ago
jrstevens
84
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
For a M/G/$infty$ queue (parameter of M is $lambda=1$), we are given that G ~ U(0,3). My goal is to find the probability that there is no one waiting in the queue at time t = 10. So far, I have broken down the problem into two non-homogeneous Poisson processes: $N(t) = W(t) + D(t)$, where W is the number of people waiting and D is the number of people already departed. An incoming customer at time s is classified as D(t) if service time is less than t -s and similarly is classified as W(t) if service time is greater than t-s. This is where I ran into trouble: computing the closed form for $lambda(t)$. Once I have this, I could apply the fact that W(t) is a non-homogeneous Poisson process to easily find $P(W(10)=0)$
probability stochastic-processes poisson-process queueing-theory
asked 2 days ago
jrstevens
84
For a M/G/$infty$ queue (parameter of M is $lambda=1$), we are given that G ~ U(0,3). My goal is to find the probability that there is no one waiting in the queue at time t = 10. So far, I have broken down the problem into two non-homogeneous Poisson processes: $N(t) = W(t) + D(t)$, where W is the number of people waiting and D is the number of people already departed. An incoming customer at time s is classified as D(t) if service time is less than t -s and similarly is classified as W(t) if service time is greater than t-s. This is where I ran into trouble: computing the closed form for $lambda(t)$. Once I have this, I could apply the fact that W(t) is a non-homogeneous Poisson process to easily find $P(W(10)=0)$
probability stochastic-processes poisson-process queueing-theory
probability stochastic-processes poisson-process queueing-theory
asked 2 days ago
jrstevens
84
asked 2 days ago
jrstevens
84
asked 2 days ago
jrstevens
84
asked 2 days ago
jrstevens
84
asked 2 days ago
jrstevens
84
84
add a comment |
add a comment |
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