# Question

Consider a single-server queueing system with a finite queue that can hold a maximum of 2 customers excluding any being served. The server can provide batch service to 2 customers simultaneously, where the service time has an exponential distribution with a mean of 1 unit of time regardless of the number being served. Whenever the queue is not full, customers arrive individually according to a Poisson process at a mean rate of 1 per unit of time.

(a) Assume that the server must serve 2 customers simultaneously. Thus, if the server is idle when only 1 customer is in the system, the server must wait for another arrival before beginning service. Formulate the queueing model in terms of transitions that only involve exponential distributions by defining the appropriate states and then constructing the rate diagram. Give the balance equations, but do not solve further.

(b) Now assume that the batch size for a service is 2 only if 2 customers are in the queue when the server finishes the preceding service. Thus, if the server is idle when only 1 customer is in the system, the server must serve this single customer, and any subsequent arrivals must wait in the queue until service is completed for this customer. Formulate the result in queueing model in terms of transitions that only involve exponential distributions by defining the appropriate states and then constructing the rate diagram. Give the balance equations, but do not solve further.

(a) Assume that the server must serve 2 customers simultaneously. Thus, if the server is idle when only 1 customer is in the system, the server must wait for another arrival before beginning service. Formulate the queueing model in terms of transitions that only involve exponential distributions by defining the appropriate states and then constructing the rate diagram. Give the balance equations, but do not solve further.

(b) Now assume that the batch size for a service is 2 only if 2 customers are in the queue when the server finishes the preceding service. Thus, if the server is idle when only 1 customer is in the system, the server must serve this single customer, and any subsequent arrivals must wait in the queue until service is completed for this customer. Formulate the result in queueing model in terms of transitions that only involve exponential distributions by defining the appropriate states and then constructing the rate diagram. Give the balance equations, but do not solve further.

## Answer to relevant Questions

Consider a queueing system that has two classes of customers, two clerks providing service, and no queue. Potential customers from each class arrive according to a Poisson process, with a mean arrival rate of 10 customers ...Customers arrive at a single-server queueing system according to a Poisson process at a mean rate of 10 per hour. If the server works continuously, the number of customers that can be served in an hour has a Poisson ...Kenichi Kaneko is the manager of a production department which uses 400 boxes of rivets per year. To hold down his inventory level, Kenichi has been ordering only 50 boxes each time. However, the supplier of rivets now is ...Consider a three-echelon inventory system that fits the model for a serial multiechelon system presented in Sec. 18.5, where the model parameters for this particular system are given below. Tim Madsen is the purchasing agent for Computer Center, a large discount computer store. He has recently added the hottest new computer, the Power model, to the store’s stock of goods. Sales of this model now are running ...Post your question

0