Solving Exponential Distributions with Preemptive Queueing
$begingroup$
A router implements a preemptive priority queueing policy, where high priority packets are served
first, and their arrival interrupts low priority packets’ service. If the service is interrupted, the packet is dropped. The
service time of packets is an exponential variable with rate µ=4 pkt/s. The input traffic to a router has interarrival
time distributed according to an exponential distribution with rate λ1=2 pkt/s (high priority) and λ2=1 pkt/s (low
priority). At time t=0, a packet (packet A) is being served by the router. Assume that only one more packet arrives
in the router’s buffer (packet B), that is, no more packets arrive after this packet. Note that packet A and B can be
either high or low priority. a) compute the probability that the service of packet A is interrupted. b) compute the
time from the arrival of packet B to the time it leaves the system
Just to be completely transparent, I have no idea where to even start solving this problem. I think that in the case that packet A is a high priority one, then it will not be interrupted. In the case it is low priority, it will be interrupted only if packet B is a high priority packet. So I think the first step is to calculate what is the probability that packet A is a high priority and what is the probability that packet B is a low priority and then go from there. If anyone knows how to solve these types of problems and can give a thorough explanation I would appreciate it very much.
exponential-distribution queueing-theory
asked Dec 14 '18 at 8:03
user2560035user2560035
34
$endgroup$
add a comment |
$begingroup$
A router implements a preemptive priority queueing policy, where high priority packets are served
first, and their arrival interrupts low priority packets’ service. If the service is interrupted, the packet is dropped. The
service time of packets is an exponential variable with rate µ=4 pkt/s. The input traffic to a router has interarrival
time distributed according to an exponential distribution with rate λ1=2 pkt/s (high priority) and λ2=1 pkt/s (low
priority). At time t=0, a packet (packet A) is being served by the router. Assume that only one more packet arrives
in the router’s buffer (packet B), that is, no more packets arrive after this packet. Note that packet A and B can be
either high or low priority. a) compute the probability that the service of packet A is interrupted. b) compute the
time from the arrival of packet B to the time it leaves the system
Just to be completely transparent, I have no idea where to even start solving this problem. I think that in the case that packet A is a high priority one, then it will not be interrupted. In the case it is low priority, it will be interrupted only if packet B is a high priority packet. So I think the first step is to calculate what is the probability that packet A is a high priority and what is the probability that packet B is a low priority and then go from there. If anyone knows how to solve these types of problems and can give a thorough explanation I would appreciate it very much.
exponential-distribution queueing-theory
asked Dec 14 '18 at 8:03
user2560035user2560035
34
$endgroup$
add a comment |
$begingroup$
A router implements a preemptive priority queueing policy, where high priority packets are served
first, and their arrival interrupts low priority packets’ service. If the service is interrupted, the packet is dropped. The
service time of packets is an exponential variable with rate µ=4 pkt/s. The input traffic to a router has interarrival
time distributed according to an exponential distribution with rate λ1=2 pkt/s (high priority) and λ2=1 pkt/s (low
priority). At time t=0, a packet (packet A) is being served by the router. Assume that only one more packet arrives
in the router’s buffer (packet B), that is, no more packets arrive after this packet. Note that packet A and B can be
either high or low priority. a) compute the probability that the service of packet A is interrupted. b) compute the
time from the arrival of packet B to the time it leaves the system
Just to be completely transparent, I have no idea where to even start solving this problem. I think that in the case that packet A is a high priority one, then it will not be interrupted. In the case it is low priority, it will be interrupted only if packet B is a high priority packet. So I think the first step is to calculate what is the probability that packet A is a high priority and what is the probability that packet B is a low priority and then go from there. If anyone knows how to solve these types of problems and can give a thorough explanation I would appreciate it very much.
exponential-distribution queueing-theory
asked Dec 14 '18 at 8:03
user2560035user2560035
34
$endgroup$
A router implements a preemptive priority queueing policy, where high priority packets are served
first, and their arrival interrupts low priority packets’ service. If the service is interrupted, the packet is dropped. The
service time of packets is an exponential variable with rate µ=4 pkt/s. The input traffic to a router has interarrival
time distributed according to an exponential distribution with rate λ1=2 pkt/s (high priority) and λ2=1 pkt/s (low
priority). At time t=0, a packet (packet A) is being served by the router. Assume that only one more packet arrives
in the router’s buffer (packet B), that is, no more packets arrive after this packet. Note that packet A and B can be
either high or low priority. a) compute the probability that the service of packet A is interrupted. b) compute the
time from the arrival of packet B to the time it leaves the system
Just to be completely transparent, I have no idea where to even start solving this problem. I think that in the case that packet A is a high priority one, then it will not be interrupted. In the case it is low priority, it will be interrupted only if packet B is a high priority packet. So I think the first step is to calculate what is the probability that packet A is a high priority and what is the probability that packet B is a low priority and then go from there. If anyone knows how to solve these types of problems and can give a thorough explanation I would appreciate it very much.
exponential-distribution queueing-theory
exponential-distribution queueing-theory
asked Dec 14 '18 at 8:03
user2560035user2560035
34
asked Dec 14 '18 at 8:03
user2560035user2560035
34
asked Dec 14 '18 at 8:03
user2560035user2560035
34
asked Dec 14 '18 at 8:03
user2560035user2560035
34
asked Dec 14 '18 at 8:03
user2560035user2560035
34
34
add a comment |
add a comment |
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