M & M's Queuing System

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Queue is a line of things or persons that is formed when the demand for a service or a product exceeds the supply
Your waiting time depends upon the number of costumers in line or in the queue, the number of servers, and the service time of each costumer takes to be able to complete the service they want.

There are different models in queuing system:
Single Server Model is when there is one queue and a single server.
Multiple-Server Model is when there is one waiting line and multiple servers are in parallel.

Catalog companies such L. L. Bean and Lands’ End are one of the largest company in the United States. During the holidays or peak seasons, both companies receive the most calls.

They use queuing system to make different choices including
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The service time of the doctors are distributed exponentially.
4. The number of queue is infinite.
5. The doctors are working at their full capacity
6. The average arrival rate of patients is greater than the average service rate of the doctors.
7. The servers are only the doctors and not the other medical personnel.
8. The service rate of the doctors is independent of the length of the queue.

The method that they used in this study is the M/M/S Queuing Model
. It is assumed that in this model that the arrival of the patients are in poisson probability distribution and in a first-come, first-served basis by any of the doctors. To assess and define the optimum number of doctors in the system, the service cost and waiting time cost of the costumers must be taken into consideration

TORA software was applied to compute the performance measures of multi-servers in the Healthcare Center using the following data:
1. Arrival rate of the patients = 52 patients/ hour
2. Service rate of the doctors = 6 patients/ hour
3. The number of doctors = 10

The result showed that the best server level at the healthcare center is when there are 12 doctors and the patient’s average waiting time is also
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Case 1: Multi-Queue, Multi-Server Sellers will fix a single price for all of its queue.
Case 2: The seller will include a time-cost based price discrimination by charging a separate price in each queue.

Using the Mixed Strategy Nash Equilibrium (MSNE), the results from all four treatments (Uniform, Discriminatorily, Random and Patient) are as follows:

Aggregate Treatment effects between Discriminatory and Uniform
 Price based express checkout lowers the market prices and reduces the seller’s profits.
 Consumer welfare is higher with price based express checkout.

Firm-Type Specific Treatment effects between Discriminatory and Uniform
 The single line seller is competing with the lower price of the two-line seller.
 The price of the two-line seller is reduced.

Testing the Theoretical Predictions with the Random Treatments
 The prices for both are expected to be lower in Random compared to Discriminatory Treatments.

Results of Manipulation Check – Patient Treatment
 All customers can select the lowest price line, no one will hesitate and the length of the line is irrelevant.

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