Newt Philly needs to decide where to get a haircut. He has narrowed the choice d
ID: 462450 • Letter: N
Question
Newt Philly needs to decide where to get a haircut. He has narrowed the choice down to two local hair salons – Large Hair Salon (LHS) and Small Hair Cutters (SHC). During busy periods, a new customer walks into LHS every 15 minutes (with the standard deviation of 15 minutes). At SHC, a customer walks in every hour (with the standard deviation of 1 hour). LHS has a staff of 4 barbers, while SHC has 1 barber. A typical service time at either salon lasts 30 minutes (with the standard deviation of 30 minutes). (a) If Newt walks into LHS during a busy period, how long will he wait in line before he can see a barber? (b) If Newt goes to SHC, how long will he wait in line before his haircut starts? (c) LHS just bought out SHC. LHS then closed SHC and continue to hire a barber at SHC. Suppose that all the customers who had been served at SHC will be served at LHS. Then, in this new system, how long will a customer need to wait in line before the customer can see a barber?
Explanation / Answer
a) In case of LHS,
a = average inter arrival time = 15 min.
p = average activity time = 30 min.
Utilization = u = p/a*m = 30/15*4 = 0.5 min.
as, m = 4(barbers)
Time in queue = Activity time/m * {Utilization[2(m+1)- 1]/1- Utilization} * {CVa2 + CVp2 /2}
= p/m * {u/1-u} * {CVa2 + CVp2 /2}
= 30/4 * {0.5[2(4+1)-1/ 1-0.5} * {1 + 1 / 2}
= 3.35 min.
b) In case of SHC,
a = average inter arrival time = 60 min.
p = average activity time = 30 min.
Utilization = u = p/a*m = 30/60*1 = 0.5 min.
as, m = 1(barbers)
Time in queue = Activity time/m * {Utilization[2(m+1)- 1]/1- Utilization} * {CVa2 + CVp2 /2}
= p/m * {u/1-u} * {CVa2 + CVp2 /2}