A mini telco service booth can hold up to six customers. The arrival of the customer...

   

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A mini telco service booth can hold up to six customers. The arrival of the customer follows Poisson process with a rate of A customers per hour. Customers who arrive when the service booth is full will leave without waiting for receiving a service. Whenever there are two or fewer customers at the service booth, there is only one attendant serving them. The time to service each customer is exponentially distributed with a mean of 1/μ hours. Then, whenever there are three or more customers, the attendant is joined by a colleague, and the service time is still the same for each customer. When the number of customers in the facility goes down to 2, the last attendant to complete service will stop serving. Thus, whenever there are 2 or less customers at the service booth, only one attendant can serve. (a) Draw the state-transition-rate diagram of the process. [ 4 marks] (b) Determine the local balance of the process by letting P as the limiting-state probability that the process is in state k and p = X/. [ 4 marks] (c) Determine the probability that an arriving customer leaves without receiving a service. [4 marks ] (d) Determine the probability that both attendants are busy attending the customers. [4 marks ] [ 4 marks] (e) Determine the probability that neither attendant is busy. A mini telco service booth can hold up to six customers. The arrival of the customer follows Poisson process with a rate of A customers per hour. Customers who arrive when the service booth is full will leave without waiting for receiving a service. Whenever there are two or fewer customers at the service booth, there is only one attendant serving them. The time to service each customer is exponentially distributed with a mean of 1/μ hours. Then, whenever there are three or more customers, the attendant is joined by a colleague, and the service time is still the same for each customer. When the number of customers in the facility goes down to 2, the last attendant to complete service will stop serving. Thus, whenever there are 2 or less customers at the service booth, only one attendant can serve. (a) Draw the state-transition-rate diagram of the process. [ 4 marks] (b) Determine the local balance of the process by letting P as the limiting-state probability that the process is in state k and p = X/. [ 4 marks] (c) Determine the probability that an arriving customer leaves without receiving a service. [4 marks ] (d) Determine the probability that both attendants are busy attending the customers. [4 marks ] [ 4 marks] (e) Determine the probability that neither attendant is busy.

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The image contains a problem statement for a queueing theory model involving a mini telco service booth Based on the problem statement I can guide you through the solution of each part a Draw the stat... View the full answer