function avg_response_time = sim_mm1_func(lambda,mu,time_end)
% COMP9334 Capacity Planning
%
% This Matlab file simulates an M/M/1 queue with
% mean arrival rate lambda and service rate mu
%
% It outputs the mean response time
%
% It has 3 input parameters:
% 1. Arrival rate lambda
% 2. Service rate mu
% 3. Simulation time Tend
%
% Chun Tung Chou, UNSW, 2015
%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Accounting parameters
%%%%%%%%%%%%%%%%%%%%%%%%%%%
response_time_cumulative = 0; % The cumulative response time
num_customer_served = 0; % number of completed customers at the end of the simulation
%
% The mean response time will be given by T/N
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Events
%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% There are two events: An arrival event and a departure event
%
% An arrival event is specified by
% next_arrival_time = the time at which the next customer arrives
% service_time_next_arrival = the service time of the next arrival
%
% A departure event is specified by
% next_departure_time = the time at which the next departure occurs
% arrival_time_next_departure = the time at which the next departing
% customer arrives at the system
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Initialising the events
%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% Initialising the arrival event
%
next_arrival_time = -log(1-rand(1))/lambda;
service_time_next_arrival = -log(1-rand(1))/mu;
%
% Initialise the departure event to empty
% Note: We use Inf (= infinity) to denote an empty departure event
%
next_departure_time = Inf;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Initialising the Master clock, server status, queue_length,
% buffer_content
%
% server_status = 1 if busy, 0 if idle
%
% queue_length is the number of customers in the buffer
%
% buffer_content is a matrix with 2 columns
% buffer_content(k,1) (i.e. k-th row, 1st column of buffer_content)
% contains the arrival time of the k-th customer in the buffer
% buffer_content(k,2) (i.e. k-th row, 2nd column of buffer_content)
% contains the service time of the k-th customer in the buffer
% The buffer_content is to imitate a first-come first-serve queue
% The 1st row has information on the 1st customer in the queue etc
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% Intialise the master clock
master_clock = 0;
%
% Intialise server status
server_busy = 0;
%
% Initialise buffer
buffer_content = [];
queue_length = 0;
% Start iteration until the end time
while (master_clock < time_end)
% Find out whether the next event is an arrival or depature
%
% We use next_event_type = 1 for arrival and 0 for departure
%
if (next_arrival_time < next_departure_time)
next_event_time = next_arrival_time;
next_event_type = 1;
else
next_event_time = next_departure_time;
next_event_type = 0;
end
%
% update master clock
%
master_clock = next_event_time;
%
% take actions depending on the event type
%
if (next_event_type == 1) % an arrival
if server_busy
%
% add customer to buffer_content and
% increment queue length
%
buffer_content = [buffer_content ; next_arrival_time service_time_next_arrival];
queue_length = queue_length + 1;
else % server not busy
%
% Schedule departure event with
% the departure time is arrival time + service time
% Also, set server_busy to 1
%
next_departure_time = next_arrival_time + service_time_next_arrival;
arrival_time_next_departure = next_arrival_time;
server_busy = 1;
end
% generate a new job and schedule its arrival
next_arrival_time = master_clock - log(1-rand(1))/lambda;
service_time_next_arrival = -log(1-rand(1))/mu;
else % a departure
%
% Update the variables:
% 1) Cumulative response time T
% 2) Number of departed customers N
%
response_time_cumulative = response_time_cumulative + master_clock - arrival_time_next_departure;
num_customer_served = num_customer_served + 1;
%
if queue_length % buffer not empty
%
% schedule the next departure event using the first customer
% in the buffer, i.e. use the 1st row in buffer_content
%
next_departure_time = master_clock + buffer_content(1,2);
arrival_time_next_departure = buffer_content(1,1);
%
% remove customer from buffer and decrement queue length
%
buffer_content(1,:) = [];
queue_length = queue_length - 1;
else % buffer empty
next_departure_time = Inf;
server_busy = 0;
end
end
end
avg_response_time = response_time_cumulative/num_customer_served;
% The mean response time
% disp(['The mean response time is ',num2str(Tavg)])