| (a)Operation Characteristics For Single Employee | (b)Operation Charecteristics for Two Employee |
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| Assumptions: |
| Assumptions: | Poisson Arrivals, Exponential Service Time |
| Poisson Arrivals, Exponential Service Time | The service rate is same for both servers |
| |
| Arrival Rate (l) | 0.05 | Arrival Rate (l) |
| Service Rate(μ) | 0.5 | Service Rate(μ) |
| No of Servers |
| Operation Charateristics |
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| (a)The probability that no units are in the system: | =(1-0.05/0.5) | 0.9 | The probability that no units are in the system(P0): |
| The average number of units in the waiting line: | =0.05^2/(0.5*(0.5-0.05)) | 0.011111111 | The average number of units in the waiting line: |
| The average number of units in the system: | =0.011111+(0.05/0.5) | 0.111111 | The average number of units in the system: |
| The average time a unit spends in the waiting line: | =0.011111/0.05 | 0.22222 | The average time a unit spends in the waiting line: |
| The average time a unit spends in the system: | =0.22222+(1/0.5) | 2.22222 | The average time a unit spends in the system: |
| The probability that an arriving unit has to wait for service: | =0.05/0.5 | 0.1 |
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| Total Money Spent= 20+(0.011111*0.22222*80) | 20.19752691 | Total Money Spent |
| Part (c ) |
| Therefore single employee system is more economical, as more money is spent in the two employee model |
