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In a waiting line system where the total service rate is greater than the customer arrival rate (λ < c μ), the average number of customers in service is:

A. smaller than the number of servers c
B. equal to the number of servers c
C. greater than the number of servers c
D. Any of the above is possible

User Eyayaw
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Final answer:

In a waiting line system with a total service rate larger than the arrival rate, the average number of customers in service is typically smaller than the number of servers (c).

Step-by-step explanation:

In a waiting line system where the total service rate (μ) is greater than the customer arrival rate (λ), which means λ < cμ, the average number of customers in service is typically smaller than the number of servers (c). This scenario indicates that the system has enough capacity to handle customers as they arrive, and some servers may be idle at times.

When the service rate per server (μ) multiplied by the number of servers (c) exceeds the arrival rate (λ), it means the system can serve customers at a pace that prevents queues from growing indefinitely, given a steady state is achieved.

User Nijin Narayanan
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