7. (15 marks) Data packets arrive (with Poisson distribution) to a pool of 4 modems with the arrival rate of 20 packets

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7 15 Marks Data Packets Arrive With Poisson Distribution To A Pool Of 4 Modems With The Arrival Rate Of 20 Packets 1 (232.8 KiB) Viewed 85 times

7. (15 marks) Data packets arrive (with Poisson distribution) to a pool of 4 modems with the arrival rate of 20 packets per second (A = 20). Each modem has a service rate of 10 packets per sec (u = 10). Note that there are no buffers (or queues) in the system, and hence, packets that find all modems reserved get blocked (Hint: the system presented is an M/M/4/4 system) (a) Draw the state diagram of the system with the corresponding transition rates. (b) Derive the state probabilities of the above system at equilibrium. (c) What is the probability that a connection attempt fails due to blocking? (Hint: Use the expression for the blocking probability derived in part (a)) (d) What is the blocking probability if the number of modems is increased to 6? To get the marks you need to include all the necessary calculations and explanations in your answer.