Question: Consider a single-server queueing system where interarrival times have an exponential distribution with parameter and service times have an exponential distribution with parameter .

Consider a single-server queueing system where interarrival times have an exponential with parameter λ and service times have an exponential with parameter μ. In addition, customers renege (leave the queueing system without being served) if their waiting time in the queue grows too large. In particular, assume that the time each customer is willing to wait in the queue before reneging has an exponential with a mean of 1/θ.
(a) Construct the rate diagram for this queueing system.
(b) Develop the balance equations.

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