# Question: A certain small grocery store has a single checkout stand

A certain small grocery store has a single checkout stand with a full-time cashier. Customers arrive at the stand “randomly” (i.e., a Poisson input process) at a mean rate of 30 per hour. When there is only one customer at the stand, she is processed by the cashier alone, with an expected service time of 1.5 minutes. However, the stock boy has been given standard instructions that whenever there is more than one customer at the stand, he is to help the cashier by bagging the groceries. This help reduces the expected time required to process a customer to 1 minute. In both cases, the service-time distribution is exponential.

(a) Construct the rate diagram for this queueing system.

(b) What is the steady-state probability distribution of the number of customers at the checkout stand?

(c) Derive L for this system.

(a) Construct the rate diagram for this queueing system.

(b) What is the steady-state probability distribution of the number of customers at the checkout stand?

(c) Derive L for this system.

## Relevant Questions

A department has one word-processing operator. Documents produced in the department are delivered for word processing according to a Poisson process with an expected interarrival time of 20 minutes. When the operator has ...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a mean arrival rate of 10 customers ...Suppose that the demand for a product is 30 units per month and the items are withdrawn at a constant rate. The setup cost each time a production run is undertaken to replenish inventory is $15. The production cost is $1 per ...Consider an inventory system that fits the model for a serial two-echelon system presented in Sec. 18.5, where K1 = $15,000, K2 = $500, h1 = $20, h2 = $22, and d = 5,000. Develop a table like Table 18.1 that shows the ...Suppose that production planning is to be done for the next 5 months, where the respective demands are r1 = 2, r2 = 4, r3 = 2, r4 = 2, and r5 = 3. The setup cost is $4,000, the unit production cos is $1,000, and the unit ...Post your question