Computer and Communication Networks (paperback)
| 1. | Each buffered output line of a data demultiplexer receives a block of packets every 20 µ s and keeps them in the buffer. A sequencer checks each block for any packet misordering and corrects it, if necessary. It takes 10 µ s to identify any packet misordering at each block and 30 µ s to make the right sequence if there is any packet misordering. Suppose that a buffer is initially empty and that the numbers of misorderings in the first 15 blocks are 2, 4, 0, 0, 1, 4, 3, 5, 2, 4, 0, 2, 5, 2, 1.
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| 2. | A buffered router presented by an M/M/ 1 model receives Markovian traffic with a mean packet-arrival rate of » =40/sec and an overall utilization of = 0.9.
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| 3. | For an M/M/ 1 system with service rate µ , the distribution of service time is exponential and is equal to e - µt . In other words, by letting T be a random variable to represent the time until the next packet departure , P [ T > t ] = e - µt . Now, consider an M/M/a system with i servers busy at a time, equal service rate µ per server, and a similar definition of random variable T .
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| 4. | Consider a network node represented by an M/M/ 1 model.
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| 5. | For an M/M/ 1 queueing system:
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| 6. | Consider a network node modeled by an M/M/ 1 queue in which a packet's willingness to join the queue is impacted by the queue size . A packet that finds i ˆˆ{0, 1, ...} other packets in the system joins the queue with probability
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| 7. | In an M/M/ 2 communication node, packets arrive according to a Poisson process of rate 18 per second. The system has two parallel crossbar switches, and each switch spends an exponentially distributed amount of time with mean 100 ms to process a packet.
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| 8. | Consider a high-speed node of a data network having parallel-plane switching fabrics , in which six packets can be processed at a time without any prior waiting time ( M/M/ 6 / 6). Assume that the arrival rate is 100 packets/sec and that the mean service rate is 20 packets/sec.
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| 9. | When a wireless user moves to a new cell , a handoff request for a new channel is needed. A handoff can be modeled with traffic type i assumption. When all the channels are used or none are available, the handoff call has to be terminated or blocked in the new base station. Classify the traffic into k types. Each call uses only one channel, and each channel uses only one radio channel. The handoff process at the new base station is modeled using an M/M/c/c system: random interarrival call time, exponential holding time of a channel, c channels, and c handoff calls. Let » i be the handoff request rate for traffic type i ˆˆ{0, 1, ..., k }, and let 1/ µ i be the mean channel-exchange time for traffic type i . When j channels are busy, handoff calls depart at rate j µ i . When all c i channels are in use, the channel-exchange rate is c i µ i . In this case, any new arriving handoff calls are blocked.
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| 10. | Continuing the previous exercise, we want to obtain some statistical performance-evaluation results for the handoff.
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| 11. | Consider a router containing four networked queueing nodes, each represented by an M/M/ 1 model, as shown in Figure 11.25. Any percentage number shown on each branch expresses the share of the branch from the traffic coming to its branching point. The arrival rate to the system is ± = 20 packets per ms. The service rates in these nodes are µ 1 = 100, µ 2 = 100, µ 3 = 20, and µ 4 = 30 packets per ms, respectively.
Figure 11.25. Exercise 11 network example
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| 12. | Figure 11.26 shows a network of four data switching nodes modeled by four M/M/ 1 systems. The arrival rate to this network is » . The outgoing packets get distributed over the outgoing link and feedback paths with the probabilities indicated on the figure. The arrival rate to the system is ± = 200 packets per second, and the service rates are µ 1 = 4, µ 2 = 3, µ 3 = 5, and µ = 2 packets per ms.
Figure 11.26. Exercise 12 network example
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| 13. | A network of four switching nodes is modeled by four M/M/ 1 systems, as shown in Figure 11.27. The arrival rate to the network is ± = 100 packets per second. The outgoing packets get distributed over the outgoing link and feedback paths with probabilities given on the figure.
Figure 11.27. Exercise 13 network example
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| 14. | A network of six switching nodes is modeled by six M/M/ 1 systems, as shown in Figure 11.28. Each of the five parallel nodes receives a fair share of traffic. The arrival rate to the system is ± = 200 packets per second, the service rate for the single node is µ = 100 packets per ms, and the service rate for each of the five nodes is µ i = 10 packets per ms.
Figure 11.28. Exercise 14 network example
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| 15. | A network of four routers is modeled by four M/M/ 1 systems, as shown in Figure 11.29. Outgoing packets get distributed over the outgoing link and feedback paths with the probabilities indicated on the figure. The arrival rate to the system is ± = 800 packets per second, and the service rates are µ 1 = 10, µ 2 = 12, µ 3 = 14, and µ = 16 packets per ms.
Figure 11.29. Exercise 16 network example
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| 16. | Computer simulation project . Write a computer program to simulate an input buffer of a router. Consider K = 64 buffer slots; each slot can fit only in a packet of size 1,000 bytes.
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| 17. | Computer simulation project . Carry the program you developed for a single buffer in the previous project and extend it to simulate two connected buffers: one with K 1 = 64 buffer slots and the other one with K 2 = 128 buffer slots. Each slot can fit only in a packet of size 1,000 bytes. Dynamically assign packets of different size every 1 ms, and send out the packet every t 1 seconds from the first buffer and every t 2 seconds from the second buffer:
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