Suppose packets are being routed from one computer to another and a router has a

Question

Suppose packets are being routed from one computer to another and a router has a choice of sending the packet over two different links Link A takes either 1, 2, 3, or 4 hops with equal probability before getting to the destination. Each hop takes 2 milliseconds. Link B takes 7, 8, or 9 hops with equal probability, but each of these hops only takes 1 millisecond. Let X be a random variable that represents the number of milliseconds it takes to transmit the packet from one computer to the other. a. What is the probability mass function (pm) of X over Link A? b. What is the expected time ELX1 for a packet sent over Link A? c. What is the expected time EIX1 for a packet sent over Link B? d. If the router decides to route a packet over Link A or Link B with equal probability, what is the pmf of X for both links?

Explanation / Answer

a) PMF of X over link A

Probablity(X1=2ms)=1/4, P(X2=2ms)=1/4, P(x3=2ms)=1/4, P(x4=2ms)=1/4

b) E[X]= 2*1/4+2*1/4+2*1/4+2*1/4=2

c) PMF of X over link B

P(x7=1ms)=1/3, P(x8=1ms)=1/3, P(x9=1ms)=1/3

E[X]=1*1/3+1*1/3+1*1/3=1

d) PMF for link A

P(X1/A)= P(X1)*P(A/X1)=1/4*/2=1/8 similalry for P(X2/A)=P(X2)*P(A/X2)=1/4*1/2=1/8

P(X3/A)=1/8 and P(X4/A)=1/8

PMF for link B

and for P(X7/B)=P(X7)*P(B/X7)=1/3*1/2=1/6 in similar way P(X8/B)=1/6 and P(X9/B)=1/6

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.