writing assignment week 3
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School
Wilmington University *
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Course
MBA-7730
Subject
Industrial Engineering
Date
Feb 20, 2024
Type
docx
Pages
3
Uploaded by JusticeNeutronFalcon32
1. Define the M/M/1 queue model and explain its assumptions.
The M/M/1 queue model is a queuing system characterized by memoryless arrivals (Poisson process), memoryless service times (exponential service distribution), and a single server. The assumptions include a First-Come-First-Served (FCFS) queue discipline, where customers are served in the order of their arrival. Additionally, the system assumes that arrivals and service times are independent, and the system operates under stable conditions.
2. Discuss the implications of the M/M/1 queue analysis on queue management and customer experience.
The M/M/1 queue analysis gives insights into system utilization, waiting times, and overall efficiency. High system utilization, which is much needed for resource efficiency, can lead to increased waiting times and probably customer dissatisfaction. Managing system utilization can help in attaining a balance between operational efficiency and positive customer experiences. Efficient queue management strategies, like optimizing staffing levels, can help mitigate negative customer experiences.
3. Define the M/M/2 queue model and explain its assumptions.
The M/M/2 queue model extends the M/M/1 model by introducing two servers instead of one. The assumptions remain similar, including Poisson arrivals, exponential service times, and First-Come-
First-Served queue discipline. However, the number of servers are now two, that is parallel processing of customer requests.
4. Compare the performance of an M/M/1 queue and an M/M/2 queue in terms of system utilization, waiting time, costs, and queue length for different arrival, service rates using an example.
To compare the two models, we can use an example where the arrival rate (
λ
) is 5 customers/hour, and the service rate (
μ
) for M/M/1 is 6 customers/hour, and for M/M/2, it is 12 customers/hour.
1.
System Utilization:
M/M/1: =5/6
M/M/2: = 5/12
M/M/1 has higher utilization.
2.
Waiting Time:
Waiting time in M/M/1 is higher due to lower service rate.
M/M/2 provides faster service, resulting in reduced waiting times.
3.
Costs:
M/M/1 may have lower labour costs, but higher customer dissatisfaction costs due to longer waiting times.
M/M/2 may have higher labour costs but better customer satisfaction.
4.
Queue Length:
Queue length in M/M/1 is influenced by higher arrival rates and longer service times.
M/M/2 reflects shorter queues with faster service.
5. Provide a case study or real-world example where either an M/M/1 or M/M/2 queue model was
applied and discuss the implications of the models.
In an airline ticket reservation system are used quite iften queue models. In a real- world scenario, during peak hours at a ticket checking counter, M/M/2 model with two reservation agents might be desirable to handle the increased demand. That means reduced waiting times and higher customer satisfaction. However, during low-demand hours, an M/M/1 model with a single reservation agent may be more cost-effective, even though waiting times could be longer, but it will have lower labour
costs. The choice between the 2 models in this scenario involves balancing costs, operational efficiency, and customer experience.
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