STOCHASTIC PROCESS

QUESTION 6 A store opens at 6:00. From 6:00 until 10:00, customers arrive at a Poisson rate of 20 an hour. Between 10:00 and 12:00 they arrive at a Poisson rate of 15 an hour. From 12:00 to 14:00 the arrival rate increases steadily from 15 per hour at 12:00 to 30 at 14:00. From 14:00 to 1?:00 the arrival rate drops steadily from 30 per hour at 14:00 to 25 per hour at 17:00; and from 17:00 to 19:00 the arrival rate increases from 25 at 17:00 to 40 at 19:00. Determine the expected number of customers that enter the store on a given day. QUESTION 6 IA store opens at 8:00. From 8:00 until 10:00, customers arrive at a Poisson rate of 30 an hour. Between 00:11:) and 12:00 they arrive at a Poisson rate of 25 an hour. From 12:00 to 14:00 the arrival rate increases Isteadily from 25 per hour at 12:00 to 45 at 14:00. From 14:00 to 17:00 the arrival rate drops steadily from I45 per hour at 14:00 to 30 per hour at l?:00; and from 1T:00 to 19:00 the arrival rate increases from 30 at II'HN) to 40 at 19:00. Determine the expected number of customers that enter the store on a given day. [24] \fHence, the expected number of customers who will enter the store is: 4 e. 11 13 _ m(t)=[ 20dr+f lSdr+f3 (Er30) dr+f (Er) dr+f (3+Er) d: U 4 6 2 3 3 3 11 2 2 3 1 5 \" 1 15 _ _[201]3 + [15:]E + [I2 30:] + g[131']: 41'] +_2 [115: + E! 213] l] a 2 3 l =30+(9'060)+[(240240)1(811535180)]+3[{l4306;) [1040 160)] + :13[(1495+)_(1265++18:15H 1 455 T15 = 4 _22 1 so+3o+ 5+6( 55 7511)+2( 2 + 2) =155+i+65 _@ 2 2302.5. Therefore, the expected number of customers that enter the store on a given clay is 303