Mail0081 - M Department of Industrial Engineering and...

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Unformatted text preview: M Department of Industrial Engineering and Management Indian Institute of Technology, Kharagpur End—Semester Examination Spring: 2007 Subject Operations Research (IM41082) Full Mark: 50 T liner} l-{rs (Attempt any ﬁve of the following questions) U1 1 a Derive the Pollaczek-Khintchine equation for MIG/l queue, . g b Management has to decide to give further training to a service personnel in the following queuing situation: Without training of the personnel the service is exponentially distributed with mean service time 5 minutes. With training the mean service time increases to ecreases by 30%. The arrival is Poisson 5.5 minutes but the standard deviation d and the mean arrival time is 10 per hour for both the cases. Analyze the problem 5 and make recommendation. 2 a in a MJM/l queue there is state-dependent service. The server has two rates of service, a slow rate with mean service rate y, if there are less than k person in the system and a fast rate with mean service rate ,u if there are k or more in the system. Give the form for pin in the system and show that _ k (kw!) "‘ 100:? p1 +p-p.__] l-A - 1’9 S? 7 i ‘ wherepi=iuo=£ I“: ' .u x1 = mean airival rate p” = probability of n in the system b The formula for mean length of the system mentioned above is given below: L t p {M1 Mic—opt" —kpl‘*“’i + pp.”“”tk —(rc —1)pil ‘ 0 7 '3 _ (I—m - u—m- l If the mean inter—arrival time arrival time is 30 minutes and the mean slow rate service time is 40 minutes and mean fast rate service time is 20 minutes, ﬁnd the mean waiting time and mean length of the system for the followin g two policies: i switch to high speed if there are any customers waiting 11 sw1tch to high speed when there are more than one customer is waiting ...
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