For infinite source systems, server utilization equals the service rate divided by the arrival rate.Multiple ChoiceFalseTrue

Break Down the Problem

1. Identify the key elements involved in the problem: server utilization, service rate, and arrival rate.
2. Understand the relationship between these elements in the context of infinite source systems.

Relevant Concepts

1. The formula for server utilization $\rho$ in queuing theory for infinite source systems is given by: $\rho = \frac{\mu}{\lambda}$ where: $\mu$ = service rate (the average number of customers that can be served per unit of time), $\lambda$ = arrival rate (the average number of customers arriving per unit of time).

Analysis and Detail

1. If the service rate $\mu$ is greater than the arrival rate $\lambda$, the server can handle incoming requests without getting overwhelmed, leading to a server utilization of less than 1.
2. If $\mu$ is equal to $\lambda$, the server operates at full capacity, resulting in a utilization of 1.
3. If $\mu$ is less than $\lambda$, the system becomes unstable, and the queue will grow indefinitely.

Verify and Summarize

• The statement regarding server utilization equating to the ratio of service rate to arrival rate holds true when considering an infinite source system where queuing dynamics are analyzed.
• Hence, the answer to the question is True as per the definitions and relationships established.

Final Answer

True