Creativity

Queuing System:

With observation and by experiment it is found that the cases arrive to healthcare system at random with a Poisson input process, so that interval times have an exponential distribution. Also the time spent by a doctor for each patient is like most of hospitals systems which follow an exponential distribution. So it is apparent that the M/M/S model is suitable to be used for Concordia’s university health care system.

By using experimental data it is estimated that patients arrive at average rate of 15 every hour. Each doctor spend around 30 mins for visiting the patient which mins he/she can visit 2 patients per hour. As approximately always there are 8 doctors available in the system, so 16patients can be treated each hour there. Thus with one hour as the unit of time it can be concluded that:

λ=15

µ→30minper patient→2 patients per hour 8 doctors available each hour → µ=16

So:

ρ=λμ=1516=0.9375

Average number of people in the system is:

L=λW=λμ-λ=15

Average number of people in the queue waiting to be visited is:

Lq=λWq=λ2μμ-λ=14.0625

Average time a patient spends in the system is:

W=Lλ=1515=1hour

Average time a patient waits to be visited in the queue is:

Wq=Lqλ=14.062515=0.9375 hour

So due to the calculated information above, each patient should wait around 1 hour to be visited. Also it worth mentioning that now due to the long waiting time most of students do not use university’s health care system for their regular annual checkups and test and they just use it in emergency cases.

So it is predicted that by new system more people will use health care system as it will be easier for them to use. In that case the mean arrival rate will go up which means the satisfaction of the whole system is increased, but health care system should pay attention that it will cause more average waiting time in ques and if it happens as the mean arrival rate becomes more than mean service rate, the health care system should hire more doctors...