A grocery store has one checkout counter. Customer arrive at this counter at random from 1 to 8 minutes apart and each interval time has the same probability of occurrence. The service time vary from 1 to 6 minutes, with probability give below:
| Services (minutes) | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| Probability | 0.10 | 0.20 | 0.30 | 0.25 | 0.10 | 0.05 |
a) Probability that a customer has to wait
b) Probability of a server being idle
c) Average service time
Use the following sequence of random numbers:
| Random digit for Inter-arrival time | 302 | 915 | 48 | 235 | 15 | 500 | 650 | 423 | 258 | 700 |
|---|---|---|---|---|---|---|---|---|---|---|
| Random digit for service time | 83 | 45 | 74 | 65 | 17 | 79 | 30 | 61 | 89 | 20 |
Customer arrive at this counter at random from 1 to 8 minutes apart and each interval time has the same probability of occurrence. So, Probability 1/8=0.125
| Time between arrival | Probability | Cumulative Probability | Random digit for assignment |
|---|---|---|---|
| 1 | 0.125 | 0.125 | 1-125 |
| 2 | 0.125 | 0.25 | 126-250 |
| 3 | 0.125 | 0.375 | 251-375 |
| 4 | 0.125 | 0.5 | 376-500 |
| 5 | 0.125 | 0.625 | 501-625 |
| 6 | 0.125 | 0.75 | 626-750 |
| 7 | 0.125 | 0.875 | 751-875 |
| 8 | 0.125 | 1.00 | 786-000 |
Table: Distribution time between arrival
The service time vary from 1 to 6 minutes, with probability give below:
| Services (minutes) | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| Probability | 0.10 | 0.20 | 0.30 | 0.25 | 0.10 | 0.05 |
| Service TIme | Probability | Cumulative Probability | Random digit for assignment |
|---|---|---|---|
| 1 | 0.10 | 0.10 | 1-10 |
| 2 | 0.20 | 0.30 | 11-30 |
| 3 | 0.30 | 0.60 | 31-60 |
| 4 | 0.25 | 0.85 | 61-85 |
| 5 | 0.10 | 0.95 | 86-95 |
| 6 | 0.05 | 1.00 | 96-00 |
Table: Service time distribution
#include<stdio.h>
#include<conio.h>
int total_waiting_time=0,total_idle_time=0,wait_count=0;
struct simulation{
int cust_no;
int rd_ar;
int intr_arr_time;
int arr_time;
int rd_se;
int service_begin;
int service_time;
int time_ser_end;
int waiting_time;
int idle_time;
int spend;
};
typedef struct simulation Simulation;
void schedule_arrival_time (Simulation s[],int n);
void schedule_service_time (Simulation s[],int n);
void schedule_completion_of_service (Simulation s[],int n);
int waiting_and_idle_time (Simulation s[],int n);
int schedule_spend_time(Simulation s[],int n);
void main(){
//freopen("result.txt", "r", stdin);
//freopen("result.txt", "w", stdout);
Simulation s[200];
int i,j,n,total_service_time=0;
float avg_waiting_time,probability_wait,probability_of_idle_server,avg_service_time,avg_time_btn_arrival,
avg_waiting_time_those_who_wait,Average_time_customer_spends_in_the_system;
printf(" Enter customer number: ");
scanf("%d",&n);
printf(" Enter random digit for arrival time for each customer: \n");
for(i=1;i<2;i++){
printf(" RD.Arrival[1]: -\n");
s[i].cust_no=1;
s[i].rd_ar=0;
s[i].intr_arr_time=0;
}
for(i=2;i<=n;i++){
printf(" RD.Arrival[%d]: ",i);
scanf("%d",&s[i].rd_ar);
s[i].cust_no=i;
if(s[i].rd_ar > 0 && s[i].rd_ar < 126) s[i].intr_arr_time=1;
else if(s[i].rd_ar > 125 && s[i].rd_ar < 251) s[i].intr_arr_time=2;
else if(s[i].rd_ar > 250 && s[i].rd_ar < 376) s[i].intr_arr_time=3;
else if(s[i].rd_ar > 375 && s[i].rd_ar < 501) s[i].intr_arr_time=4;
else if(s[i].rd_ar > 500 && s[i].rd_ar < 626) s[i].intr_arr_time=5;
else if(s[i].rd_ar > 625 && s[i].rd_ar < 751) s[i].intr_arr_time=6;
else if(s[i].rd_ar > 750 && s[i].rd_ar < 876) s[i].intr_arr_time=7;
else if(s[i].rd_ar > 875 && s[i].rd_ar < 1001) s[i].intr_arr_time=8;
else{printf(" Warning!! Please Enter RD. around 1-1000"); return 0;}
}
schedule_arrival_time( s, n);
printf(" Enter random digit for service time for each customer: \n");
for(i=1;i<2;i++){
s[i].service_begin=0;
}
for(i=1;i<=n;i++){
printf(" RD.Service[%d]: ",i);
scanf("%d",&s[i].rd_se);
if(s[i].rd_se > 0 && s[i].rd_se < 11) s[i].service_time=1;
else if(s[i].rd_se > 10 && s[i].rd_se < 31) s[i].service_time=2;
else if(s[i].rd_se > 30 && s[i].rd_se < 61) s[i].service_time=3;
else if(s[i].rd_se > 60 && s[i].rd_se < 86) s[i].service_time=4;
else if(s[i].rd_se > 85 && s[i].rd_se < 96) s[i].service_time=5;
else if(s[i].rd_se > 95 && s[i].rd_se < 101) s[i].service_time=6;
else{printf(" Warning!! Please Enter RD. around 1-100"); return 0;}
total_service_time+=s[i].service_time;
}
schedule_service_time( s, n);
schedule_completion_of_service( s, n);
schedule_service_time( s, n);
schedule_completion_of_service( s, n);
waiting_and_idle_time( s, n);
int total_spend_time = schedule_spend_time(s, n);
printf("\n ------------------------------------------------------------------------------------------------------------------");
printf("\n | Cust.| RD. for | Inter_arrival | Arrival | RD. for | Service | T.Service| T.Service| Waiting | Server | Spend in |\n");
printf(" | No. |Arrival.T| Time | Time |Service.T| Time | Begin | End | in Queue| Idle.T | System |");
printf("\n ------------------------------------------------------------------------------------------------------------------\n");
for(i=1; i<=n; i++){
printf(" %d %d %d %d %d %d %d %d %d %d %d\n"
,s[i].cust_no,s[i].rd_ar,s[i].intr_arr_time,s[i].arr_time,s[i].rd_se,s[i].service_time,s[i].service_begin,
s[i].time_ser_end,s[i].waiting_time,s[i].idle_time,s[i].spend);
if(i!=n){
printf(" ------------------------------------------------------------------------------------------------------------------\n");
}
else{
printf(" --------------------------------------------------------====----------------------------====------====-----====--\n");
}
}
printf("\t\t\t\t\t\t\t %d \t\t\t\t %d \t %d\t%d",
total_service_time,total_waiting_time,total_idle_time,total_spend_time);
avg_waiting_time = (float)total_waiting_time/(float)n;
probability_wait = (float)wait_count/(float)n;
probability_of_idle_server = (float)total_idle_time/(float)s[n].time_ser_end;
avg_service_time = (float)total_service_time/(float)n;
avg_time_btn_arrival = (float)s[n].arr_time/(float)(n-1);
avg_waiting_time_those_who_wait = (float)total_waiting_time/(float)wait_count;
Average_time_customer_spends_in_the_system = (float)total_spend_time/(float)n;
printf("\n Average waiting time = %.2f",avg_waiting_time);
printf("\n Probability(wait) = %.2f",probability_wait);
printf("\n Probability of idle server = %.2f",probability_of_idle_server);
printf("\n Average service time = %.2f",avg_service_time);
printf("\n Average time between arrival= %.2f",avg_time_btn_arrival);
printf("\n Average waiting time of those who wait= %.2f",avg_waiting_time_those_who_wait);
printf("\n Average time customer spends in the system= %.2f",Average_time_customer_spends_in_the_system);
printf("\n\n\n\n");
return 0;
}
void schedule_arrival_time (Simulation s[],int n){
int i;
for( i=2; i<=n; i++){
s[i].arr_time=s[i-1].arr_time+s[i].intr_arr_time;
}
}
void schedule_service_time (Simulation s[],int n){
int i;
for( i=2; i<=n; i++){
if(s[i].arr_time > s[i-1].time_ser_end){
s[i].service_begin=s[i].arr_time;
}
else{
s[i].service_begin=s[i-1].time_ser_end;
}
}
}
void schedule_completion_of_service (Simulation s[],int n){
int i;
for( i=1; i<=n; i++){
s[i].time_ser_end=s[i].service_begin+s[i].service_time;
}
}
int waiting_and_idle_time (Simulation s[],int n ){
int i;
s[1].waiting_time=0;
s[1].idle_time=0;
for( i=2; i<=n; i++){
if(s[i].arr_time > s[i-1].time_ser_end){
s[i].idle_time=s[i].arr_time-s[i-1].time_ser_end;
total_idle_time+=s[i].idle_time;
s[i].waiting_time=0;
}
else{
s[i].waiting_time=s[i-1].time_ser_end-s[i].arr_time;
total_waiting_time+=s[i].waiting_time;
s[i].idle_time=0;
}
if(s[i].waiting_time!=0){
wait_count=wait_count+1;
}
}
}
int schedule_spend_time (Simulation s[],int n){
int i,aa, total_spend_time=0;
for(i=1;i<=n;i++)
{
s[i].spend = s[i].service_time+s[i].waiting_time;
total_spend_time+=s[i].spend;
}
return total_spend_time;
}
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