STATS 320 Applied Stochastic Modelling
Assignment 3
Due 4 pm, Monday May 18, 2009
1
Patients arrive at an emergency clinic as a Poisson process at rate 5 per hour.
The clinic is staffed by one doctor, and a consultation takes a period of time that
is uniformly distributed on the interval [5
,
15) minutes. All interarrival times
and service times are independent of one another. The queueing discipline is
first come first served, and you may assume that the queue is operating in steady
state.
a
Describe this queue using the Kendall
A

S

m

n
notation.
b
Determine the following quantities:
i
L
, the expected number of patients at the clinic (including those being
seen by the doctor) in steady state
ii
L
q
, the expected number of patients in the waiting room, waiting to
see the doctor, in steady state
iii
L
s
, the expected number of patients being seen by the doctor, in steady
state.
iv
W
,
W
q
and
W
s
.
c
What is the expected length of a busy period for the doctor?
(A busy
period commences when a patient arrives after an idle period, and finishes
when the doctor is next idle again.)
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '09
 renate
 Poisson Distribution, Probability theory, M C C

Click to edit the document details