**Exercise 2.2.**

Draw the traffic profile of a periodic ON-OFF source characterized by the following parameters:

• average rate, ,

• capacity of a data block (data issued in the active source state), ,

• inactivity period, .

**Exercise 2.4.**

Draw the traffic profile of a periodic ON-OFF source characterized by the following parameters:

• ratio between duration of activity and inactivity periods, ,

• time interval between two consecutive source transitions from the ON state to the OFF state, ,

• total amount of data issued in an interval of , .

**Exercise 2.7.**

Consider a one-way ring network consisting of 4 nodes X, Y, Z, W, connected in series. The
X-Y, Y-Z, Z-W and W-X connections between adjacent nodes have a capacity C bit/s. Assuming that each
node receives traffic from a CBR source and that all sources offer traffic with the same peak rate P, determine
the maximum throughput that characterizes this network and the maximum rate Pmax that does not
cause traffic losses.

**Exercise 2.11.**

A source A generates a flow of IUs obtained by encoding a voice signal CBR at a peak rate by silence suppression. For simplicity, it is assumed that silence pauses (of constant duration ) alternate with speech intervals (of constant duration ) and each silence pause involves the removal of from the data stream. Source A therefore behaves as a periodic VBR ON-OFF source
with burstiness factor BA = 0.375. The source is connected by means of a link of negligible length to a packet
transmission node X. The IUs received by A, after a processing delay equal to 2/3 of , are retransmitted
by X as packets to destination B without adding any overhead and without any queueing delay. Node X transmits
at peak rate . B is a space module in orbit around the Moon and is located at an approximate distance from X . Calculate the total transfer time from A to B of the IUs issued by the source in the interval [0,40] s, also graphically representing with the correct scale ratios: (i) the flow of IUs issued by A (), (ii) the flow of IUs issued by X (), (iii) the flow of IUs received by B ().

**Exercise 2.15.**

Two terminal stations A and B are connected by a link crossing two packet-switched nodes X
and Z with the following numerical values:

• capacity of the two access links A-X and Z-B, ,

• capacity of the internode link X-Z, ,

• length of the two access links A-X and Z-B, ,

• length of the internode link X-Z, ,

• signal propagation speed on all connections, ,

• processing times in nodes X and Z, and .

Assuming an infinite storage capacity in the nodes, calculate the total end-to-end delay required for the transmission from A to B of a 10,000-byte data unit which is broken into two packets of equal length with a packet header (no other data units cross the nodes X and Z).

**Exercise 2.17.**

Determine the symbolic expression analogous to Equation 2.6 which provides the total time required to transmit and receive (completely) a sequence of N packets of equal length from a source S to a destination D along a path that crosses H nodes, . All nodes are characterized by the same parameters (transmission time of a packet), (processing time of a packet), and all the links are characterized by the same delay . The nodes are assumed to have infinite storage capacity and no other data units pass through the nodes.

**Exercise 2.20.**

Consider a cascade of 3 packet switched nodes, A, B, C, connected by cable and characterized
by the following parameters on the respective outgoing connections: , , , . Node A issues packets of constant length at rate . Assuming that node B starts to retransmit a packet immediately after receiving it completely and that its processing time is zero, calculate the overall delay for the transmission of 3 packets from A to C.

**Exercise 2.26.**

Consider a packet switched network topology with 6 nodes (A, B, C, D, E, F) and 7 edges (AB,
B-C, C-D, D-E, F-A, B-E, C-F) with virtual circuit service where the following virtual connections are
active:

1 H-A-B-C-H

2 H-A-B-C-D-H

3 H-F-C-D-H

4 H-E-B-C-D-H

5 H-D-C-B-A-H

6 H-E-B-A-H

Fill in the forwarding tables of the nodes assuming that:

• the connections have been established in the order of the list,

• the logical channel identifier has 2 bits available,

• the logical channel identifier assigned by each node/host is the smallest available.

**Exercise 2.30.**

An S-TDM synchronous multiplexer generates an output flow with rate , frames of period which include 36 traffic time slots each, each with capacity of n bits, and an alignment time slot whose capacity is half of that available in a traffic slot. Determine the frame length and the capacity available in each traffic time slot.