sketch a 5-input, 3-output switching element. time is slotted and synchronized for inputs. One slot holds at most one packet. A packet arrival processes to each input are Bernoulli (with arrival probability p for a packet in each slot and non arrival probability 1-p in each slot) (a) write an expression for the probability of one or more arrivals in a slot. (b) find the throughput at the output (c) write an expression for the probability in a slot that the top 3 inputs have packets and the bottom 2 doesn't have a packet. (d) for what values of p is the probability of 2 arrivals at the input greater than the probability of ine arrival at the inputs?
sketch a 5-input, 3-output switching element. time is slotted and synchronized for inputs. One slot holds at most one packet. A packet arrival processes to each input are Bernoulli (with arrival probability p for a packet in each slot and non arrival probability 1-p in each slot) (a) write an expression for the probability of one or more arrivals in a slot. (b) find the throughput at the output (c) write an expression for the probability in a slot that the top 3 inputs have packets and the bottom 2 doesn't have a packet. (d) for what values of p is the probability of 2 arrivals at the input greater than the probability of ine arrival at the inputs?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
![sketch a 5-input, 3-output switching element. time
is slotted and synchronized for inputs. One slot
holds at most one packet. A packet arrival
processes to each input are Bernoulli (with arrival
probability p for a packet in each slot and non
arrival probability 1-p in each slot)
(a) write an expression for the probability of one or
more arrivals in a slot.
(b) find the throughput at the output
(c) write an expression for the probability in a slot
that the top 3 inputs have packets and the bottom
2 doesn't have a packet.
(d) for what values of p is the probability of 2
arrivals at the input greater than the probability of
ine arrival at the inputs?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff6cc09c2-f05e-43f8-a8a5-2414f8e5baab%2Fdb0b94c6-c8f1-41f6-bf67-986705874d76%2F9cwmhch_processed.jpeg&w=3840&q=75)
Transcribed Image Text:sketch a 5-input, 3-output switching element. time
is slotted and synchronized for inputs. One slot
holds at most one packet. A packet arrival
processes to each input are Bernoulli (with arrival
probability p for a packet in each slot and non
arrival probability 1-p in each slot)
(a) write an expression for the probability of one or
more arrivals in a slot.
(b) find the throughput at the output
(c) write an expression for the probability in a slot
that the top 3 inputs have packets and the bottom
2 doesn't have a packet.
(d) for what values of p is the probability of 2
arrivals at the input greater than the probability of
ine arrival at the inputs?
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