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In a finance firm, there are 7 back-end financial analysts serving requests of traders to perform detailed financial analysis. On average, the traders send a request to the analysts in every 5 minutes. It takes one analyst half an hour to finish the analysis for a request. Every minute the trader waits for the analysis results costs the company $10,000 because of delay in trading.


a. On average, how many requests are there waiting to be served by the analysts?


b. How long does it take, on average, for a trader to receive detailed analysis for his/her request?


c. On average, what is the hourly cost to the company because of traders awaiting analysis results?


[Each question worth 5 points]

Respuesta :

letmeanswer

Solution and Explanation:

Average arrival rate, λ = 1 in 5 minutes = 12 per hour

Average service rate, μ = 1 in 30 minutes = 2 per hour

Number of servers, s = 7

(a)  Use the following two formulae to compute the idle server probability (P0) and the average number of requests waiting (Lq):

(Please see the attached file)  

Use the known values of λ, μ, and s, to get the following:

P0 = 0.0016

Lq = 3.68

So, the average number of requests waiting to be served = 3.68

(b)  Average waiting time [tex], W_{q}=L_{q} / \lambda=3.68 / 12[/tex] = 0.307 hours = 18.4 minutes.  So,  The average time required for a trader to receive detailed analysis, Ws = Wq + service time = 18.4+30 = 48.4 minutes

(c)  Hourly cost of waiting = [tex]\mathrm{W}_{s} * \lambda * \$ 10,000=48.4 * 12 * 10000[/tex] = $5,808,000

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