quantitive method

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q_and_q_4_.xlsx
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Sheet1

Assumptions of M/M/s M/D/1 Constant service time like automatic car wash or an amusement park ride. M/G/1 General service time like auto repair shop or a sales clerk. M/M/S/∞/N Finite population size
1. Arivals are served on a FIFO basis.
2. No balking or reneging The average wait time for constant service is half that of the expotential variable service. Equipment repair in a factory with 5 machines
3. Arrivals are independent and the arrival rate constant
4. Arrivals follow a Poisson distribution. Assumptions:
5. Service times are independent with a fixed average. 1. There are s servers with identical service time distributions.
6. Service times follow an exponential distribution. 2. The population of units seeking service is finite, of size N.
7. μ x s > λ implies a finite queue length. - the number in the queue is a significant proportion of the arrival population.
3. λ = average number of arrivals per time period
λ = average number of arrivals per time period λ = average number of arrivals per time period λ = average number of arrivals per time period 4. μ = average number of people or items served per time period.
1. ρ = utilization factor of the system μ = average number of people or items served per time period. μ = constant # of people or items served per time period. μ = average number of people or items served per time period. 5. λ and μ are specified for the same time period.
2. Lq = average length of the queue s = # of servers σ = standard deviation of service time. 6. FIFO
3. L = average number of customers in the system
4. Wq = average time each customer spends in the queue
5. W = average time that each customer spends in the system. λ = per period λ = per hour λ = per hour λ =
6. P0 = the probability that there are no customers in the system. μ = per period μ = per hour μ = per hour ERROR:#DIV/0! μ =
7. Pn = probability that there are exactly n customers in the system s = s = σ = per hour s =
N =
Key operating characteristics of a queuing system Key operating characteristics of a queuing system Key operating characteristics of a queuing system Key operating characteristics of a queuing system
1. ρ = ERROR:#DIV/0! 1. ρ = ERROR:#DIV/0! 1. ρ = ERROR:#DIV/0! 1. ρ = ERROR:#DIV/0!
2. P0 = ERROR:#N/A 2. Lq = ERROR:#DIV/0! Twice as fast as M 2. Lq = ERROR:#DIV/0! 2. Lq = ERROR:#DIV/0!
3. Lq = ERROR:#DIV/0! ERROR:#DIV/0! 3. L = ERROR:#DIV/0! 3. L = ERROR:#DIV/0! 3. L = ERROR:#DIV/0!
4. L = ERROR:#DIV/0! ERROR:#DIV/0! 4. Wq = ERROR:#DIV/0! hours ERROR:#DIV/0! 4. Wq = ERROR:#DIV/0! hours ERROR:#DIV/0! 4. Wq = ERROR:#DIV/0!
5. Wq = ERROR:#DIV/0! period ERROR:#DIV/0! 5. W = ERROR:#DIV/0! hours ERROR:#DIV/0! 5. W = ERROR:#DIV/0! hours ERROR:#DIV/0! 5. W = ERROR:#DIV/0!
6. W = ERROR:#DIV/0! period ERROR:#DIV/0! 6. P0 = ERROR:#DIV/0! 6. P0 = ERROR:#DIV/0! 6. P0 = ERROR:#DIV/0!
Effective arrival rate ERROR:#DIV/0!
Cumulative Cumulative
n Pn Prob (1/k!)(λ/μ)k Probabilities
0 ERROR:#N/A ERROR:#N/A ERROR:#DIV/0! Cumulative ERROR:#DIV/0!
1 ERROR:#N/A ERROR:#N/A ERROR:#DIV/0! n Pn Prob Number waiting Arrival rate(n) Term 1 Sum term 1 Term 2 Sum term 2 Decum term 2 P0(s)
2 ERROR:#N/A ERROR:#N/A ERROR:#DIV/0! 0 ERROR:#DIV/0! ERROR:#DIV/0! 0 0 ERROR:#DIV/0! ERROR:#DIV/0! ERROR:#DIV/0! ERROR:#DIV/0! ERROR:#DIV/0! ERROR:#DIV/0!
3 ERROR:#N/A ERROR:#N/A ERROR:#DIV/0! 1
4 ERROR:#N/A ERROR:#N/A ERROR:#DIV/0! 2
5 ERROR:#N/A ERROR:#N/A ERROR:#DIV/0! 3
6 ERROR:#N/A ERROR:#N/A ERROR:#DIV/0! 4
7 ERROR:#N/A ERROR:#N/A ERROR:#DIV/0! 5
8 ERROR:#N/A ERROR:#N/A ERROR:#DIV/0! 6
9 ERROR:#N/A ERROR:#N/A ERROR:#DIV/0! 7
10 ERROR:#N/A ERROR:#N/A ERROR:#DIV/0! 8
11 ERROR:#N/A ERROR:#N/A ERROR:#DIV/0! 9
12 ERROR:#N/A ERROR:#N/A 10
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Sheet2

Assumptions of M/M/s M/D/1 Constant service time like automatic car wash or an amusement park ride. M/G/1 General service time like auto repair shop or a sales clerk. M/M/S/∞/N Finite population size
1. Arivals are served on a FIFO basis.
2. No balking or reneging The average wait time for constant service is half that of the expotential variable service. Equipment repair in a factory with 5 machines
3. Arrivals are independent and the arrival rate constant
4. Arrivals follow a Poisson distribution. Assumptions:
5. Service times are independent with a fixed average. 1. There are s servers with identical service time distributions.
6. Service times follow an exponential distribution. 2. The population of units seeking service is finite, of size N.
7. μ x s > λ implies a finite queue length. - the number in the queue is a significant proportion of the arrival population.
3. λ = average number of arrivals per time period
λ = average number of arrivals per time period λ = average number of arrivals per time period λ = average number of arrivals per time period 4. μ = average number of people or items served per time period.
1. ρ = utilization factor of the system μ = average number of people or items served per time period. μ = constant # of people or items served per time period. μ = average number of people or items served per time period. 5. λ and μ are specified for the same time period.
2. Lq = average length of the queue s = # of servers σ = standard deviation of service time. 6. FIFO
3. L = average number of customers in the system
4. Wq = average time each customer spends in the queue
5. W = average time that each customer spends in the system. λ = per period λ = per hour λ = per hour λ =
6. P0 = the probability that there are no customers in the system. μ = per period μ = per hour μ = per hour ERROR:#DIV/0! μ =
7. Pn = probability that there are exactly n customers in the system s = s = σ = per hour s =
N =
Key operating characteristics of a queuing system Key operating characteristics of a queuing system Key operating characteristics of a queuing system Key operating characteristics of a queuing system
1. ρ = ERROR:#DIV/0! 1. ρ = ERROR:#DIV/0! 1. ρ = ERROR:#DIV/0! 1. ρ = ERROR:#DIV/0!
2. P0 = ERROR:#N/A 2. Lq = ERROR:#DIV/0! Twice as fast as M 2. Lq = ERROR:#DIV/0! 2. Lq = ERROR:#DIV/0!
3. Lq = ERROR:#DIV/0! ERROR:#DIV/0! 3. L = ERROR:#DIV/0! 3. L = ERROR:#DIV/0! 3. L = ERROR:#DIV/0!
4. L = ERROR:#DIV/0! ERROR:#DIV/0! 4. Wq = ERROR:#DIV/0! hours ERROR:#DIV/0! 4. Wq = ERROR:#DIV/0! hours ERROR:#DIV/0! 4. Wq = ERROR:#DIV/0!
5. Wq = ERROR:#DIV/0! period ERROR:#DIV/0! 5. W = ERROR:#DIV/0! hours ERROR:#DIV/0! 5. W = ERROR:#DIV/0! hours ERROR:#DIV/0! 5. W = ERROR:#DIV/0!
6. W = ERROR:#DIV/0! period ERROR:#DIV/0! 6. P0 = ERROR:#DIV/0! 6. P0 = ERROR:#DIV/0! 6. P0 = ERROR:#DIV/0!
Effective arrival rate ERROR:#DIV/0!
Cumulative Cumulative
n Pn Prob (1/k!)(λ/μ)k Probabilities
0 ERROR:#N/A ERROR:#N/A ERROR:#DIV/0! Cumulative ERROR:#DIV/0!
1 ERROR:#N/A ERROR:#N/A ERROR:#DIV/0! n Pn Prob Number waiting Arrival rate(n) Term 1 Sum term 1 Term 2 Sum term 2 Decum term 2 P0(s)
2 ERROR:#N/A ERROR:#N/A ERROR:#DIV/0! 0 ERROR:#DIV/0! ERROR:#DIV/0! 0 0 ERROR:#DIV/0! ERROR:#DIV/0! ERROR:#DIV/0! ERROR:#DIV/0! ERROR:#DIV/0! ERROR:#DIV/0!
3 ERROR:#N/A ERROR:#N/A ERROR:#DIV/0! 1
4 ERROR:#N/A ERROR:#N/A ERROR:#DIV/0! 2
5 ERROR:#N/A ERROR:#N/A ERROR:#DIV/0! 3
6 ERROR:#N/A ERROR:#N/A ERROR:#DIV/0! 4
7 ERROR:#N/A ERROR:#N/A ERROR:#DIV/0! 5
8 ERROR:#N/A ERROR:#N/A ERROR:#DIV/0! 6
9 ERROR:#N/A ERROR:#N/A ERROR:#DIV/0! 7
10 ERROR:#N/A ERROR:#N/A ERROR:#DIV/0! 8
11 ERROR:#N/A ERROR:#N/A ERROR:#DIV/0! 9
12 ERROR:#N/A ERROR:#N/A 10
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