# Packet and Circuit Switching, and Little's Law

• Packet and Circuit Switching, and Little’s Law discussion and Problem solutions.

• Sender and receiver are separated by two 1-Gigabit/s links and a single switch. The packet size is 5000 bits, and each link introduces a propagation delay of 10 microseconds. Assume that the switch begins forwarding immediately after it has received the last bit of the packet and the queues are empty.

For each link, it takes 1 Gigabits/5 Kbits = 5 microseconds to transmit the packet on the link, after which it takes an additional 10 microseconds for the last bit to propagate across the link. Thus, with only one switch that starts forwarding only after receiving the whole packet, the total transfer delay is two transmit delays + two propagation delays = 30 microseconds.

• Sender and receiver are separated by two 1-Gigabit/s links and a single switch. The packet size is 5000 bits, and each link introduces a propagation delay of 10 microseconds. Assume that the switch begins forwarding immediately after it has received the last bit of the packet and the queues are empty.

• A fast-food restaurant uses 3,500 kilograms of hamburger each week. The manager of the restaurant wants to ensure that the meat is always fresh, i.e., the meat should be no more than two days old on average when used. How much hamburger should be kept in the refrigerator as inventory?

Rate = 3,500 kilograms per week (= 500 kilograms per day)
Average flow time = 2 days
Average inventory = Rate x Average flow time = 500 x 2 = 1,000 kilograms
(Note that the variables are all in the same time frame i.e. days)

• A fast-food restaurant uses 3,500 kilograms of hamburger each week. The manager of the restaurant wants to ensure that the meat is always fresh, i.e., the meat should be no more than two days old on average when used. How much hamburger should be kept in the refrigerator as inventory?

• A restaurant holds about 60 people, and the average person will be in there about 2 hours. On average, how many customers arrive per hour? If the restaurant queue has 30 people waiting to be seated, how long does each person have to wait for a table?

Rate = 60 customers / 2 hrs = 30 customers / hr
Waiting time = 1 hour

• A restaurant holds about 60 people, and the average person will be in there about 2 hours. On average, how many customers arrive per hour? If the restaurant queue has 30 people waiting to be seated, how long does each person have to wait for a table?

• At the supermarket a checkout operator has on average 4 customers and customers arrive every 2 minutes. How long must each customer wait in line on average?

Throughput time = 4 customers / 1/2 customer/minute = 8 minutes

• At the supermarket a checkout operator has on average 4 customers and customers arrive every 2 minutes. How long must each customer wait in line on average?

5

1

5

2

9

2

2

4
| |