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The expected waiting time in system for typical truck is 2 hours.
Step-by-step explanation:
Data Given are as follows.
Truck arrival rate is given by, α = 36 / day
Truck operation departure rate is given, β= 48 / day
A constructed queuing model is such that so that queue lengths and waiting time can be predicted.
In queuing theory, we have to achieve economic balance between number of customers arriving into system and that of leaving the system whether referring to people or things, in correlating such variables as how customers arrive, how service meets their requirements, average service time and extent of variations, and idle time.
This problem is solved by using concept of Single Channel Arrival with exponential service infinite populate model.
Waiting time in system is given by,
where is waiting time in system
is arrival rate described Poission distribution
is service rate described by Exponential distribution
...it is due to 1 day = 24 hours
Therefore, time required for waiting in system is 2 hours.
Answer:
Step-by-step explanation:
The population of a community is known to increase at a rate proportional to the number of people present at time t.
This means that the population growth is modeled by the following differential equation:
Which has the following solution:
In which P(t) is the population after t years, P(0) is the initial population and r is the growth rate.
The population has doubled in 10 years
This means that . We use this to find r.
So the equation that will estimate the population of the community in t years is: