Question: 1. Consider a pure loss system with 10 servers. The average service time is 3 min. It is also known that the average number of
1. Consider a pure loss system with 10 servers. The average service time is 3 min. It is also known that the average number of customers in the system is 7.0 and an arriving customer is lost with probability of 14%. Determine the total arrival rate of new customers (including both those who enter the system and those who are lost)? 2. Consider a pure single server queueing system with average service rate of 2.5 customers/s. New customers arrive at rate 2.0 customers/s. The average total delay is 3.0 s (including both the waiting time and the service time). a. What is the average number of customers in the whole system? b. What is the average number of waiting customers? c. What is the average number of customers in service? d. What is the average number of departing customers during an interval of length 10 s? 3. According to measurements, there are, on average, 1000 packets in a subnetwork. This subnetwork is connected with the rest of the trunk network via four nodes. The arrival rates of packets (coming from the rest) to these four nodes are 1 = 200, 2 = 300, 3 = 400, and 4 = 500 packets/s, respectively. Determine the average time that a packet spends in the subnetwork.
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