EECS 148 Introduction to Computer Networks
Problem Set #7
** NOTE: The "Walrand 1st ed." problems are on the "Non-textbook problems" handout. The "Walrand 2nd ed." problems are in your textbook.
Walrand 1st ed. #1.6: Note that the question asks "how often".
Walrand 1st ed. #2.12: The denominator for B given should read "1 + rho + rho^2 / 2! + ...". The "1" was missing on the scanned copy. You should be able to solve for N=1 and N=2 on paper. You will need to write a spreadsheet or program to solve for N=3 and N=4. (Some spreadsheets however may have difficulty calculating factorials of large numbers.) Interpret your answer for N=1.
Walrand 1st ed. #2.14: (a) "Draw a diagram ..." - This should be a graph showing the number of bits in the buffer as a function of time. (b) "Using your diagram ..." - Write an expression for the delay from the time until the 1st packet arrives until its transmission is complete. Write similar expressions for the 2nd and 3rd packets. (c) "Give a simple condition ..." - Give me mathematical expressions that if true will result in the queueing times to be 0. (d) "Exhibit arrival times ..." - Draw a function, as in part (a), showing your choice of arrival times for at least 10 packets and the resulting buffer content.
Walrand 2nd ed. Appendix A, #4: Hint - The first question is asking the probability that exactly 1 of the N stations attempts to transmit in a particular time slot.
Walrand 2nd ed. Appendix A, #5: "The connection is working if and only if one of the two links is up" - Interpret this to mean if and only if at least one of the two links is up. "Generalize to an arbitrary topology" - ignore this part.