Sally Gordon Has Just Completed Her MBA Degree and Is

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The Answer is (a)This is an M/M/s queueing system.The mean arrival rate is

\lambda

= 30 customers per hour.The mean service rate is

\mu

= (60 min/hr)/ (3 minutes/customer)= 20 customers per hour.The number of servers is s = 2.The Template for the M/M/s queueing model is shown below.The average waiting time for a customer before reaching a teller is W_q = 0.064 hours = 3.86 minutes.The average number of customers in the bank,including those currently being served,is L = 3.43. $(a)This is an M/M/s queueing system.The mean arrival rate is \lambda = 30 customers per hour.The mean service rate is \mu = (60 min/hr)/ (3 minutes/customer)= 20 customers per hour.The number of servers is s = 2.The Template for the M/M/s queueing model is shown below.The average waiting time for a customer before reaching a teller is Wq = 0.064 hours = 3.86 minutes.The average number of customers in the bank,including those currently being served,is L = 3.43. (b)As in part a,this is an M/M/s queueing system with mean arrival rate \lambda = 30 customers per hour and mean service rate \mu = 20 customers per hour.To satisfy the company policy that there be no more than a 10% chance that a customer will need to wait more than 5 minutes before reaching a teller,we need to assure that Pr(Wq > t)in cell C11 is no more than 10% when t = 0.0833 hours (5 minutes).From part a,when s = 2,Pr(Wq > t)= 27.9%.As shown below,when s = 3,Pr(Wq > t)= 1.9%.Thus,First Bank will need at least 3 tellers to meet this standard. (c)This question can be answered using the template for economic analysis of the M/M/s queueing model.The cost of service is Cs = $18/hour/server.The cost of waiting is Cw = $0.50/minute/server = $30/hour/server.The total cost of service and waiting is Cs s + Cw L.As seen in the templates below,with 2 servers the total cost is $138.86.With 3 servers,the total cost is $106.11.With 4 servers the total cost is $118.34.Therefore,Sally should employ 3 servers. (d)The queueing systems for merchant and regular customers are two separate,but identical,M/M/s queueing systems.For each,the mean arrival rate is \lambda = 15 customers per hour.The mean service rate is \mu = 20 customers per hour.The number of servers is s = 1.The template for the M/M/s queueing model is shown below.The average waiting time for a customer before reaching a teller is Wq = 0.15 hours = 9 minutes.The average number of customers of each type in the bank,including those currently being served,is L = 3.Thus,the total number of customers (of both types)is 6.These results are significantly worse than those from part a.(e)Like part d,the queueing systems for merchant and regular customers are two separate,but identical,M/M/s queueing systems.For each,the mean arrival rate is \lambda = 15 customers per hour.The mean service rate is \mu = (60 min/hr)/ (2.5 minutes/customer)= 24 customers per hour.The number of servers is s = 1.The template for the M/M/s queueing model is shown below.The average waiting time for a customer before reaching a teller is Wq = 0.069 hours = 4.17 minutes.The average number of customers of each type in the bank,including those currently being served,is L = 1.67.Thus,the total number of customers (of both types)is 3.33.These results are similar to those from part a.The waiting time before reaching a teller is slightly higher (4.17 minutes vs.3.86 minutes),but the total number of customers in the bank is slightly smaller (3.33 vs.3.43)$
(b)As in part a,this is an M/M/s queueing system with mean arrival rate

\lambda

= 30 customers per hour and mean service rate

\mu

= 20 customers per hour.To satisfy the company policy that there be no more than a 10% chance that a customer will need to wait more than 5 minutes before reaching a teller,we need to assure that Pr(W_q > t)in cell C11 is no more than 10% when t = 0.0833 hours (5 minutes).From part a,when s = 2,Pr(W_q > t)= 27.9%.As shown below,when s = 3,Pr(W_q > t)= 1.9%.Thus,First Bank will need at least 3 tellers to meet this standard. $(a)This is an M/M/s queueing system.The mean arrival rate is \lambda = 30 customers per hour.The mean service rate is \mu = (60 min/hr)/ (3 minutes/customer)= 20 customers per hour.The number of servers is s = 2.The Template for the M/M/s queueing model is shown below.The average waiting time for a customer before reaching a teller is Wq = 0.064 hours = 3.86 minutes.The average number of customers in the bank,including those currently being served,is L = 3.43. (b)As in part a,this is an M/M/s queueing system with mean arrival rate \lambda = 30 customers per hour and mean service rate \mu = 20 customers per hour.To satisfy the company policy that there be no more than a 10% chance that a customer will need to wait more than 5 minutes before reaching a teller,we need to assure that Pr(Wq > t)in cell C11 is no more than 10% when t = 0.0833 hours (5 minutes).From part a,when s = 2,Pr(Wq > t)= 27.9%.As shown below,when s = 3,Pr(Wq > t)= 1.9%.Thus,First Bank will need at least 3 tellers to meet this standard. (c)This question can be answered using the template for economic analysis of the M/M/s queueing model.The cost of service is Cs = $18/hour/server.The cost of waiting is Cw = $0.50/minute/server = $30/hour/server.The total cost of service and waiting is Cs s + Cw L.As seen in the templates below,with 2 servers the total cost is $138.86.With 3 servers,the total cost is $106.11.With 4 servers the total cost is $118.34.Therefore,Sally should employ 3 servers. (d)The queueing systems for merchant and regular customers are two separate,but identical,M/M/s queueing systems.For each,the mean arrival rate is \lambda = 15 customers per hour.The mean service rate is \mu = 20 customers per hour.The number of servers is s = 1.The template for the M/M/s queueing model is shown below.The average waiting time for a customer before reaching a teller is Wq = 0.15 hours = 9 minutes.The average number of customers of each type in the bank,including those currently being served,is L = 3.Thus,the total number of customers (of both types)is 6.These results are significantly worse than those from part a.(e)Like part d,the queueing systems for merchant and regular customers are two separate,but identical,M/M/s queueing systems.For each,the mean arrival rate is \lambda = 15 customers per hour.The mean service rate is \mu = (60 min/hr)/ (2.5 minutes/customer)= 24 customers per hour.The number of servers is s = 1.The template for the M/M/s queueing model is shown below.The average waiting time for a customer before reaching a teller is Wq = 0.069 hours = 4.17 minutes.The average number of customers of each type in the bank,including those currently being served,is L = 1.67.Thus,the total number of customers (of both types)is 3.33.These results are similar to those from part a.The waiting time before reaching a teller is slightly higher (4.17 minutes vs.3.86 minutes),but the total number of customers in the bank is slightly smaller (3.33 vs.3.43)$
(c)This question can be answered using the template for economic analysis of the M/M/s queueing model.The cost of service is C_s = $18/hour/server.The cost of waiting is C_w = $0.50/minute/server = $30/hour/server.The total cost of service and waiting is C_s s + C_w L.As seen in the templates below,with 2 servers the total cost is $138.86.With 3 servers,the total cost is $106.11.With 4 servers the total cost is $118.34.Therefore,Sally should employ 3 servers. $(a)This is an M/M/s queueing system.The mean arrival rate is \lambda = 30 customers per hour.The mean service rate is \mu = (60 min/hr)/ (3 minutes/customer)= 20 customers per hour.The number of servers is s = 2.The Template for the M/M/s queueing model is shown below.The average waiting time for a customer before reaching a teller is Wq = 0.064 hours = 3.86 minutes.The average number of customers in the bank,including those currently being served,is L = 3.43. (b)As in part a,this is an M/M/s queueing system with mean arrival rate \lambda = 30 customers per hour and mean service rate \mu = 20 customers per hour.To satisfy the company policy that there be no more than a 10% chance that a customer will need to wait more than 5 minutes before reaching a teller,we need to assure that Pr(Wq > t)in cell C11 is no more than 10% when t = 0.0833 hours (5 minutes).From part a,when s = 2,Pr(Wq > t)= 27.9%.As shown below,when s = 3,Pr(Wq > t)= 1.9%.Thus,First Bank will need at least 3 tellers to meet this standard. (c)This question can be answered using the template for economic analysis of the M/M/s queueing model.The cost of service is Cs = $18/hour/server.The cost of waiting is Cw = $0.50/minute/server = $30/hour/server.The total cost of service and waiting is Cs s + Cw L.As seen in the templates below,with 2 servers the total cost is $138.86.With 3 servers,the total cost is $106.11.With 4 servers the total cost is $118.34.Therefore,Sally should employ 3 servers. (d)The queueing systems for merchant and regular customers are two separate,but identical,M/M/s queueing systems.For each,the mean arrival rate is \lambda = 15 customers per hour.The mean service rate is \mu = 20 customers per hour.The number of servers is s = 1.The template for the M/M/s queueing model is shown below.The average waiting time for a customer before reaching a teller is Wq = 0.15 hours = 9 minutes.The average number of customers of each type in the bank,including those currently being served,is L = 3.Thus,the total number of customers (of both types)is 6.These results are significantly worse than those from part a.(e)Like part d,the queueing systems for merchant and regular customers are two separate,but identical,M/M/s queueing systems.For each,the mean arrival rate is \lambda = 15 customers per hour.The mean service rate is \mu = (60 min/hr)/ (2.5 minutes/customer)= 24 customers per hour.The number of servers is s = 1.The template for the M/M/s queueing model is shown below.The average waiting time for a customer before reaching a teller is Wq = 0.069 hours = 4.17 minutes.The average number of customers of each type in the bank,including those currently being served,is L = 1.67.Thus,the total number of customers (of both types)is 3.33.These results are similar to those from part a.The waiting time before reaching a teller is slightly higher (4.17 minutes vs.3.86 minutes),but the total number of customers in the bank is slightly smaller (3.33 vs.3.43)$ $(a)This is an M/M/s queueing system.The mean arrival rate is \lambda = 30 customers per hour.The mean service rate is \mu = (60 min/hr)/ (3 minutes/customer)= 20 customers per hour.The number of servers is s = 2.The Template for the M/M/s queueing model is shown below.The average waiting time for a customer before reaching a teller is Wq = 0.064 hours = 3.86 minutes.The average number of customers in the bank,including those currently being served,is L = 3.43. (b)As in part a,this is an M/M/s queueing system with mean arrival rate \lambda = 30 customers per hour and mean service rate \mu = 20 customers per hour.To satisfy the company policy that there be no more than a 10% chance that a customer will need to wait more than 5 minutes before reaching a teller,we need to assure that Pr(Wq > t)in cell C11 is no more than 10% when t = 0.0833 hours (5 minutes).From part a,when s = 2,Pr(Wq > t)= 27.9%.As shown below,when s = 3,Pr(Wq > t)= 1.9%.Thus,First Bank will need at least 3 tellers to meet this standard. (c)This question can be answered using the template for economic analysis of the M/M/s queueing model.The cost of service is Cs = $18/hour/server.The cost of waiting is Cw = $0.50/minute/server = $30/hour/server.The total cost of service and waiting is Cs s + Cw L.As seen in the templates below,with 2 servers the total cost is $138.86.With 3 servers,the total cost is $106.11.With 4 servers the total cost is $118.34.Therefore,Sally should employ 3 servers. (d)The queueing systems for merchant and regular customers are two separate,but identical,M/M/s queueing systems.For each,the mean arrival rate is \lambda = 15 customers per hour.The mean service rate is \mu = 20 customers per hour.The number of servers is s = 1.The template for the M/M/s queueing model is shown below.The average waiting time for a customer before reaching a teller is Wq = 0.15 hours = 9 minutes.The average number of customers of each type in the bank,including those currently being served,is L = 3.Thus,the total number of customers (of both types)is 6.These results are significantly worse than those from part a.(e)Like part d,the queueing systems for merchant and regular customers are two separate,but identical,M/M/s queueing systems.For each,the mean arrival rate is \lambda = 15 customers per hour.The mean service rate is \mu = (60 min/hr)/ (2.5 minutes/customer)= 24 customers per hour.The number of servers is s = 1.The template for the M/M/s queueing model is shown below.The average waiting time for a customer before reaching a teller is Wq = 0.069 hours = 4.17 minutes.The average number of customers of each type in the bank,including those currently being served,is L = 1.67.Thus,the total number of customers (of both types)is 3.33.These results are similar to those from part a.The waiting time before reaching a teller is slightly higher (4.17 minutes vs.3.86 minutes),but the total number of customers in the bank is slightly smaller (3.33 vs.3.43)$ $(a)This is an M/M/s queueing system.The mean arrival rate is \lambda = 30 customers per hour.The mean service rate is \mu = (60 min/hr)/ (3 minutes/customer)= 20 customers per hour.The number of servers is s = 2.The Template for the M/M/s queueing model is shown below.The average waiting time for a customer before reaching a teller is Wq = 0.064 hours = 3.86 minutes.The average number of customers in the bank,including those currently being served,is L = 3.43. (b)As in part a,this is an M/M/s queueing system with mean arrival rate \lambda = 30 customers per hour and mean service rate \mu = 20 customers per hour.To satisfy the company policy that there be no more than a 10% chance that a customer will need to wait more than 5 minutes before reaching a teller,we need to assure that Pr(Wq > t)in cell C11 is no more than 10% when t = 0.0833 hours (5 minutes).From part a,when s = 2,Pr(Wq > t)= 27.9%.As shown below,when s = 3,Pr(Wq > t)= 1.9%.Thus,First Bank will need at least 3 tellers to meet this standard. (c)This question can be answered using the template for economic analysis of the M/M/s queueing model.The cost of service is Cs = $18/hour/server.The cost of waiting is Cw = $0.50/minute/server = $30/hour/server.The total cost of service and waiting is Cs s + Cw L.As seen in the templates below,with 2 servers the total cost is $138.86.With 3 servers,the total cost is $106.11.With 4 servers the total cost is $118.34.Therefore,Sally should employ 3 servers. (d)The queueing systems for merchant and regular customers are two separate,but identical,M/M/s queueing systems.For each,the mean arrival rate is \lambda = 15 customers per hour.The mean service rate is \mu = 20 customers per hour.The number of servers is s = 1.The template for the M/M/s queueing model is shown below.The average waiting time for a customer before reaching a teller is Wq = 0.15 hours = 9 minutes.The average number of customers of each type in the bank,including those currently being served,is L = 3.Thus,the total number of customers (of both types)is 6.These results are significantly worse than those from part a.(e)Like part d,the queueing systems for merchant and regular customers are two separate,but identical,M/M/s queueing systems.For each,the mean arrival rate is \lambda = 15 customers per hour.The mean service rate is \mu = (60 min/hr)/ (2.5 minutes/customer)= 24 customers per hour.The number of servers is s = 1.The template for the M/M/s queueing model is shown below.The average waiting time for a customer before reaching a teller is Wq = 0.069 hours = 4.17 minutes.The average number of customers of each type in the bank,including those currently being served,is L = 1.67.Thus,the total number of customers (of both types)is 3.33.These results are similar to those from part a.The waiting time before reaching a teller is slightly higher (4.17 minutes vs.3.86 minutes),but the total number of customers in the bank is slightly smaller (3.33 vs.3.43)$
(d)The queueing systems for merchant and regular customers are two separate,but identical,M/M/s queueing systems.For each,the mean arrival rate is

\lambda

= 15 customers per hour.The mean service rate is

\mu

= 20 customers per hour.The number of servers is s = 1.The template for the M/M/s queueing model is shown below.The average waiting time for a customer before reaching a teller is W_q = 0.15 hours = 9 minutes.The average number of customers of each type in the bank,including those currently being served,is L = 3.Thus,the total number of customers (of both types)is 6.These results are significantly worse than those from part a.(e)Like part d,the queueing systems for merchant and regular customers are two separate,but identical,M/M/s queueing systems.For each,the mean arrival rate is

\lambda

= 15 customers per hour.The mean service rate is

\mu

= (60 min/hr)/ (2.5 minutes/customer)= 24 customers per hour.The number of servers is s = 1.The template for the M/M/s queueing model is shown below.The average waiting time for a customer before reaching a teller is W_q = 0.069 hours = 4.17 minutes.The average number of customers of each type in the bank,including those currently being served,is L = 1.67.Thus,the total number of customers (of both types)is 3.33.These results are similar to those from part a.The waiting time before reaching a teller is slightly higher (4.17 minutes vs.3.86 minutes),but the total number of customers in the bank is slightly smaller (3.33 vs.3.43)
$(a)This is an M/M/s queueing system.The mean arrival rate is \lambda = 30 customers per hour.The mean service rate is \mu = (60 min/hr)/ (3 minutes/customer)= 20 customers per hour.The number of servers is s = 2.The Template for the M/M/s queueing model is shown below.The average waiting time for a customer before reaching a teller is Wq = 0.064 hours = 3.86 minutes.The average number of customers in the bank,including those currently being served,is L = 3.43. (b)As in part a,this is an M/M/s queueing system with mean arrival rate \lambda = 30 customers per hour and mean service rate \mu = 20 customers per hour.To satisfy the company policy that there be no more than a 10% chance that a customer will need to wait more than 5 minutes before reaching a teller,we need to assure that Pr(Wq > t)in cell C11 is no more than 10% when t = 0.0833 hours (5 minutes).From part a,when s = 2,Pr(Wq > t)= 27.9%.As shown below,when s = 3,Pr(Wq > t)= 1.9%.Thus,First Bank will need at least 3 tellers to meet this standard. (c)This question can be answered using the template for economic analysis of the M/M/s queueing model.The cost of service is Cs = $18/hour/server.The cost of waiting is Cw = $0.50/minute/server = $30/hour/server.The total cost of service and waiting is Cs s + Cw L.As seen in the templates below,with 2 servers the total cost is $138.86.With 3 servers,the total cost is $106.11.With 4 servers the total cost is $118.34.Therefore,Sally should employ 3 servers. (d)The queueing systems for merchant and regular customers are two separate,but identical,M/M/s queueing systems.For each,the mean arrival rate is \lambda = 15 customers per hour.The mean service rate is \mu = 20 customers per hour.The number of servers is s = 1.The template for the M/M/s queueing model is shown below.The average waiting time for a customer before reaching a teller is Wq = 0.15 hours = 9 minutes.The average number of customers of each type in the bank,including those currently being served,is L = 3.Thus,the total number of customers (of both types)is 6.These results are significantly worse than those from part a.(e)Like part d,the queueing systems for merchant and regular customers are two separate,but identical,M/M/s queueing systems.For each,the mean arrival rate is \lambda = 15 customers per hour.The mean service rate is \mu = (60 min/hr)/ (2.5 minutes/customer)= 24 customers per hour.The number of servers is s = 1.The template for the M/M/s queueing model is shown below.The average waiting time for a customer before reaching a teller is Wq = 0.069 hours = 4.17 minutes.The average number of customers of each type in the bank,including those currently being served,is L = 1.67.Thus,the total number of customers (of both types)is 3.33.These results are similar to those from part a.The waiting time before reaching a teller is slightly higher (4.17 minutes vs.3.86 minutes),but the total number of customers in the bank is slightly smaller (3.33 vs.3.43)$

Sally Gordon Has Just Completed Her MBA Degree and Is

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