Exercises for Week 1
Exercise 1: Basic Delay Calculation
A data packet with a size of L = 5,000 bytes needs to be sent from a source to a destination across N
= 3 links (connected by 2 routers). The transmission rate of each link is R = 10Mbps. Ignore
propagation and queuing delays.
1. Calculate the time L/R required to push the data packet onto a single link.
2. Calculate the total end-to-end delay for the data packet to reach its destination.
Exercise 2: Determining the Number of Routers
A network transmits a data packet L = 2MB (1MB = 8 x 106 bits) at a transmission rate of R =
8Mbps on each link. Given that the total store-and-forward end-to-end delay is 10 seconds (ignore
propagation and queuing delays).
1. Calculate the number of links N along the path.
2. How many routers are on this path?
Exercise 3: Packet Segmentation / Pipelining
A data file with a total size of D = 3 MB (24 x 10 6 bits) is transmitted from a source to a destination
across N = 4 links with a transmission rate of R = 12 Mbps on each link. Ignore propagation and
queuing delays.
1. If the file is sent as 1 single packet (L = 3 MB), calculate the total end-to-end delay.
2. If the file is divided into 3 equal smaller packets (L' = 1 MB / packet), calculate the total
end-to-end delay for all 3 packets to reach the destination.
Exercise 4: Non-uniform Link Speeds (Bottleneck Link)
Send a data packet L = 10 Mb (107 bits) from a source to a destination across 3 links in series with
the following respective transmission rates:
• Link 1: R1 = 10 Mbps
• Link 2: R2 = 5 Mbps
• Link 3: R3 = 20 Mbps
Assume the network transmits only this single data packet, routers use store-and-forward
transmission, and propagation and queuing delays are ignored. Calculate the total end-to-end delay.
Exercise 5: Packet Size Optimization with Header
A data file D = 1.2 MB (1.2 x 106 bytes) needs to be transmitted across N = 5 identical links with a
transmission rate of R = 20 Mbps (20 x 106 bits/second).
The file is divided into P equal smaller data packets. Each packet, when sent, is appended with a
fixed header H = 200 bytes.
1. Derive the formula for the total end-to-end delay T(P) as a function of the number of
packets P.
2. Find the optimal number of packets P that minimizes the total end-to-end delay, and
calculate that minimum delay value. (Ignore propagation and queuing delays).