• 検索結果がありません。

2009final OR toyo_classes

N/A
N/A
Protected

Academic year: 2017

シェア "2009final OR toyo_classes"

Copied!
1
0
0

読み込み中.... (全文を見る)

全文

(1)

Operations Research

Final2009

Hiroshi Toyoizumi

7/27/2009

1. What is the queue, waiting time and the number of customers in the system? Explain them, using examples.

2. Suppose, on the average, there are 4 customers in the line at a coffee shop counter and the arrival rate to this shop is 2 customers/min. Estimate the customer’s average sojourn time in the line.

3. Let N (t) be the number of customers in the M/M/1 queue with arrival rate λ = 1 and service rate µ = 2. Set the steady state probability by

pn = lim

t→∞P {N (t) = n}. (1)

Derive the exact value of p0, p1 and p2 and draw the graph of pn. 4. Explain the differences between Produce-to-Order and Produce-to-Stock

systems.

5. Explain how you can use an M/M/1 queue to model Produce-to-Stock systems, using figures and formulas.

6. Explain how to use Linear Programing. 7. You can write anything you want.

Remark 1. Don’t write lengthy answers. Your answers should be concise and focused.

Remark 2. Each problem is 5 point worth.

1

参照

関連したドキュメント

Then it follows immediately from a suitable version of “Hensel’s Lemma” [cf., e.g., the argument of [4], Lemma 2.1] that S may be obtained, as the notation suggests, as the m A

The time-frequency integrals and the two-dimensional stationary phase method are applied to study the electromagnetic waves radiated by moving modulated sources in dispersive media..

Using the batch Markovian arrival process, the formulas for the average number of losses in a finite time interval and the stationary loss ratio are shown.. In addition,

For p = 2, the existence of a positive principal eigenvalue for more general posi- tive weights is obtained in [26] using certain capacity conditions of Maz’ja [22] and in [30]

While conducting an experiment regarding fetal move- ments as a result of Pulsed Wave Doppler (PWD) ultrasound, [8] we encountered the severe artifacts in the acquired image2.

Examining this figure reveals that for each fixed pair of values of µ and s, the average deleterious substitution rate is nearly as small as the smallest frequency-dependent rate

Yet another analysis of the model considered here is done in 24, but there it was assumed that both the arrival and service rates of the secondary customers are small, while the

In the proofs of these assertions, we write down rather explicit expressions for the bounds in order to have some qualitative idea how to achieve a good numerical control of the