Chapter 4: Understanding and Applying Waiting Line Analysis

4.1

Describe four types of waiting line systems with respect to channels and phases.

4.2

Assume your organization installed a router whose packet processing capability is 2000 per second. Based on the following packet arrival rate, draw the occupancy of the router's memory queue for times t ₁ through t ₁₀ .

Time	Packet Arrival
t ₁
t ₂	1750
t ₄	2250
t ₅	2750
t ₆	3000
t ₇	3250
t ₈	3500
t ₉	1750
t ₁₀	1500

4.3

Continuing your examination of the router service capacity and packet arrival rate described in Problem 4.2, describe what happens if the average length of a packet is 800 bytes and the router's buffer memory available for queuing packets is limited to 32,000 bytes of storage.

4.4

Assume constant arrival and service rates where the arrival rate is 10 frames/sec and the service rate is 12 frames /sec. At time (t) = 10 seconds, what is the size of the queue?

4.5

Assume the level of utilization of a service facility is 23.5 percent. What is the probability that the facility is empty?

4.6

Assume that the arrival rate of frames at a router varies as follows by seconds:

If the router service rate is fixed at 3 frames/sec, what is the router's queue length at t = 1, 2, 3, 4, and 5 seconds?

4.7

Under what conditions should you consider installing two circuits to interconnect distant locations, each operating at n/2 bps instead of one circuit operating at n bps?

4.8

Waiting Line Analysis Practical Exercise: Assume you were just hired by the industrial conglomerate McEars, Inc., as a senior network analyst. McEars has offices in Macon, Georgia, and Chicago, Illinois, and operates 100Base-T networks at each location. Currently, there is no connection between each local area network.

Your first project assignment at McEars is to determine an optimum line operating rate to interconnect the two isolated LANs. Based on an analysis of company- projected internetworking requirements, you determined the following information concerning the expected utilization of a leased line that would be installed to connect offices in Macon and Chicago:

The majority of inter-LAN communications will flow from corporate headquarters in Macon to Chicago, which enables you to select a line operating rate based on traffic flowing in that direction.
During the eight- hour workday , 600 e-mail messages can be expected to be transmitted from Macon to Chicago. The average length of an e-mail message is 1200 bytes, with 20 additional header bytes added when the message is transported on the expected wide area network (WAN) connection.
During the eight-hour workday, 20 files with an average file size of 2 Mbytes are expected to be transmitted from Macon to Chicago. Each frame transported on the WAN can be expected to have a header of 20 bytes added for the WAN protocol used to carry the frame between locations. Because the LAN frame preamble is stripped when the frame is encapsulated and transmitted on a WAN, assume that the maximum frame length on the WAN is 1538 bytes, to include the 20 bytes added by the WAN protocol.

Your assignment:

Compute the optimum line rate for a blended average of anticipated e-mail messages and file transfers during the eight-hour workday. Explain the rationale behind your line operating rate selection.
Assume you were able to determine that instead of transmission occurring randomly but evenly over an eight-hour day a significant amount of traffic to include 300 e-mail messages and ten files would be transmitted between 9 AM and 10 AM each day, representing a busy-hour period. Does this change your line operating rate selection? Explain.