# Question

Consider the following statements about an M/G/1 queueing system, where 2 is the variance of service times. Label each statement as true or false, and then justify your answer.

(a) Increasing σ2 (with fixed λ and μ) will increase Lq and L, but will not change Wq and W.

(b) When choosing between a tortoise (small μ and σ 2) and a hare (large μ and σ2) to be the server, the tortoise always wins by providing a smaller Lq.

(c) With μ and σ fixed, the value of Lq with an exponential servicetime distribution is twice as large as with constant service times.

(d) Among all possible service-time distributions (with λ and μ fixed), the exponential distribution yields the largest value of Lq.

(a) Increasing σ2 (with fixed λ and μ) will increase Lq and L, but will not change Wq and W.

(b) When choosing between a tortoise (small μ and σ 2) and a hare (large μ and σ2) to be the server, the tortoise always wins by providing a smaller Lq.

(c) With μ and σ fixed, the value of Lq with an exponential servicetime distribution is twice as large as with constant service times.

(d) Among all possible service-time distributions (with λ and μ fixed), the exponential distribution yields the largest value of Lq.

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