Q2. In Aegis life insurance company, the deposit and withdrawal functions associated with cer- tain investment product are separated by two clerks, Stack and Slack. Deposit slips arrive at Stack’s desk according to a Poisson process with a mean rate of 16 per hour. Withdrawal slips arrive at Slack’s desk according to a Poisson process with a mean rate of 14 per hour. The time required to process either transaction has an exponential distribution with a mean of 3 minutes. Based on this information, answer the following questions: (a) In the current situation, what model will you apply for analysis of queuing system at Stack’s desk and Slack’s desk? Answer this question by filling the following table. Model λ µ ρ Reaches steady state? Stack's Desk - - - - - Slack's Desk - - - - - (b) What is the expected waiting time of a deposit slip at Stack’s desk? What is the expected waiting time of a withdrawal slip at Slack’s desk? Suppose “the system” contains both Stack and Slack’s desks. Note that: P(a random arriving slip in the system is a deposit slip) = 16/30 P(a random arriving slip in the system is a withdrawal slip) = 14/30 (c) Using part (b) and the probabilities above, calculate the expected waiting time in the system for a random arrival of slip.
Q2. In Aegis life insurance company, the deposit and withdrawal functions associated with cer- tain investment product are separated by two clerks, Stack and Slack. Deposit slips arrive at Stack’s desk according to a Poisson process with a mean rate of 16 per hour. Withdrawal slips arrive at Slack’s desk according to a Poisson process with a mean rate of 14 per hour. The time required to process either transaction has an exponential distribution with a mean of 3 minutes.
Based on this information, answer the following questions:
(a) In the current situation, what model will you apply for analysis of queuing system at Stack’s desk and Slack’s desk? Answer this question by filling the following table.
| Model | λ | µ | ρ | Reaches steady state? | |
| Stack's Desk | - | - | - | - | - |
| Slack's Desk | - | - | - | - | - |
(b) What is the expected waiting time of a deposit slip at Stack’s desk? What is the expected waiting time of a withdrawal slip at Slack’s desk?
Suppose “the system” contains both Stack and Slack’s desks. Note that:
P(a random arriving slip in the system is a deposit slip) = 16/30
P(a random arriving slip in the system is a withdrawal slip) = 14/30
(c) Using part (b) and the probabilities above, calculate the expected waiting time in the system for a random arrival of slip.
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