# Question

Consider the M/G/1 model with λ = 0.2 and μ = 0.25.

T (a) Use the Excel template for this model (or hand calculations) to find the main measures of performance—L, Lq, W, Wq—for each of the following values of σ: 4, 3, 2, 1, 0.

(b) What is the ratio of Lq with σ = 4 to Lq with σ = 0? What does this say about the importance of reducing the variability of the service times?

(c) Calculate the reduction in Lq when σ is reduced from 4 to 3, from 3 to 2, from 2 to 1, and from 1 to 0. Which is the largest reduction? Which is the smallest?

(d) Use trial and error with the template to see approximately how much μ would need to be increased with σ = 4 to achieve the same Lq as with μ = 0.25 and σ = 0.

T (a) Use the Excel template for this model (or hand calculations) to find the main measures of performance—L, Lq, W, Wq—for each of the following values of σ: 4, 3, 2, 1, 0.

(b) What is the ratio of Lq with σ = 4 to Lq with σ = 0? What does this say about the importance of reducing the variability of the service times?

(c) Calculate the reduction in Lq when σ is reduced from 4 to 3, from 3 to 2, from 2 to 1, and from 1 to 0. Which is the largest reduction? Which is the smallest?

(d) Use trial and error with the template to see approximately how much μ would need to be increased with σ = 4 to achieve the same Lq as with μ = 0.25 and σ = 0.

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