A what is the utilization rate of this service system

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a. a.
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Chapter 9 Queuing Model M/M/s (Exponential Service Times) Input Data Operating Characteristics Answ Arrival rate (l) 20 Average server utilization (r) 0.6667 66.67% (a) Service rate (m) 30 Average number of customers in the queue (L q ) 1.3333 1.3333 (b) Number of servers (s) 1 Average number of customers in the system (L) 2.0000 Average waiting time in the queue (W q ) 0.0667 4 ( c Average time in the system (W) 0.1000 6 (d) Probability (% of time) system is empty (P 0 ) 0.3333 33.33% ( e Answer: a. 67% ; b. 1.33; c. 4 minutes; d. 6 minutes; e. 33.33% Probabilities Number of Units Probabilit y Cumulative Probability
COM-315 0 0.3333 0.3333 1 0.2222 0.5556 2 0.1481 0.7037 3 0.0988 0.8025 4 0.0658 0.8683 5 0.0439 0.9122 6 0.0293 0.9415 7 0.0195 0.9610 8 0.0130 0.9740 9 0.0087 0.9827 10 0.0058 0.9884 1 0

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