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Homework answers / question archive / The following questions refer to the information and output below
The following questions refer to the information and output below. The university computer lab has 10 computers which are constantly being used by students. Users need help from the one lab assistant fairly often. Students ask for help at a Poisson rate of with an average of 4 requests per hour for any one computer. The assistant answers questions as quickly as possible and the service time follows an exponential distribution with mean of 1 minute per help session. The following queuing analysis spreadsheet was developed from this information Arrival rate Service rate Number of servers Population Size 60 1 10 (max of 40) (max of 100) Utilization P(O), probability that the system is empty Lq, expected queue length L. expected number in system Wq, expected time in queue W, expected total time in system Probability that a customer waits 58.97% 0.41034 0.56545 1.15511 0.01598 0.03265 0.58966 Refer to Exhibit 13.6. What is the Kendall notation for this system?
a)
The Kendall notation for a system is generally represented as (a/b/c):(d/e)
where,
a = arrival disrtibution
b = service time distribution
c = number of servers
d = Maximum number of customers allowed in system
e = queue discipline
The symbols change according to the given conditions of queue but the sequence remains same.
/ Arrival rate can have following distribution options, that is, a can be replaced by :-
M if the arrival rate/distribution is poisson distribution
or D if the arrival distribution is deterministic interval time
The Question has stated that arrival rate follows poisson distrubion,
Hence a is replaced by M...............................................................................(1)
/ Service rate can have following distribution options, that is, b can be replaced by :-
M if the service rate follows exponential distribution or service time distrubtion
or D if the service rate follows deterministic arrival rate
or Ek if the the service rate follows Erlang K distribution
or G for general independent service
The question has stated that service rate is exponential
Hence, b is replaced by M...........................................................................(2)
/ Number of servers can be one or multiple. Only these two options are available for c :-
1 if the number of servers is one
or S if the number of servers is multiple
Here, we have only one staff attending the students
Hence c is relpaed by 1................................................................................(3)
/ Number of maximum customers allowed can be finite or infinte, the symbols for d are:
- if the maximum customers allowed is infinite
N - if the maximum customers allowed is finite
Here we can have infinite number of students coming in throught the life of computer lab,
Hence d is replaced by ..............................................................................(4)
/ the mode of sequencing can be either of following, that is e can be repalced by :-
FIFO - if the sequencing is first in first out basis
LIFO - if the sequencing is last in first out basis
SIRO - if the sequencing is in a interval of random order
GD - if the servicing is in general queue disciplin
Here, the helper services the help as soon as possible, which is first come first serve basis
Hence e is replaced by FIFO..............................................................................(5)
Combining (1),(2),(3),(4) and (5)
We have the Kendall Notation for the given sequence as (M / M / 1 ) : ( / FIFO)..........................(a)
