{
"metadata": {
"name": "",
"signature": "sha256:dd4432cc2f7e790571ec64d7a8254cb368aab6a22204c8b382ba85e3c1b5a734"
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"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 2: Teletraffic Engineering"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 2.1, Page 25"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Variable declaration\n",
"LC=10.; #Lost calls\n",
"CC=380; #Carried calls\n",
"\n",
"#Calculations\n",
"OC=LC+CC; #Total offered calls\n",
"#Gos=Blocking probability=(number of Lost calls/Total number of offered calls)\n",
"Gos=LC/OC;\n",
"\n",
"#Result\n",
"print 'The Gos during busy hour is %f \\n '%Gos"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The Gos during busy hour is 0.025641 \n",
" \n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 2.2, Page 26"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Variable declaration\n",
"Ht=5; #Average holding time in seconds\n",
"PC=450; # Peg count for one hour period\n",
"OC=0; # Overflow count\n",
"\n",
"#Calculations&Results\n",
"# usage(Erlangs)=(peg count- overflow count)*Average holding time(in hrs)\n",
"U=(PC-OC)*(5./3600); \n",
"print 'Usage = %.3f Erlangs'%U\n",
"\n",
"# IN CCS\n",
"Uccs=U*36; # usage in CCS\n",
"print '%.1f CCS'%Uccs\n",
"\n",
"Ucs=Uccs *100; #usage in call-seconds\n",
"print '%d call-seconds'%Ucs"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Usage = 0.625 Erlangs\n",
"22.5 CCS\n",
"2250 call-seconds\n"
]
}
],
"prompt_number": 5
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 2.3, Page 27"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Variable declaration\n",
"B=0.05; #Blocking(5%)\n",
"CL=3000.; #Carried Load in CCS\n",
"\n",
"#Calculations\n",
"#Offered Load=Carried Load/(1-Blocking);\n",
"OL=CL/(1-B); #Offered Load in CCS\n",
"\n",
"#Result\n",
"print 'Offered load is %d CCS'%OL\n",
"print 'Overflow is %d CCS'%((OL-CL))"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Offered load is 3157 CCS\n",
"Overflow is 157 CCS\n"
]
}
],
"prompt_number": 8
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 2.4, Page 27"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Variable declaration\n",
"Ht=120; #Holding time in seconds\n",
"CR=2.; #call rate per hour\n",
"\n",
"#Calculations\n",
"#Traffic Intensity(Erlangs) = call rate * Holding time(in hrs));\n",
"I=CR*Ht/3600; #Traffic Intensity\n",
"\n",
"#Result\n",
"print 'Traffic Intensity is %.4f Erlangs = %.1f CCS \\n'%(I,I*36);\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Traffic Intensity is 0.0667 Erlangs = 2.4 CCS \n",
"\n"
]
}
],
"prompt_number": 9
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 2.5, Page 27"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Variable declaration\n",
"time=90.; #in minutes\n",
"calls=10.; #no of calls in 90mins\n",
"\n",
"#Calculations\n",
"CR=calls/(time/60); #call arrival rate in calls/hour\n",
"tavg=(60.+74+80+90+92+70+96+48+64+126)/10; #average call holding time in sec per call\n",
"I= CR*(tavg/3600); #traffic intensity in Erlangs\n",
"\n",
"#Result\n",
"print 'Traffic Intensity is %.3f Erlangs = %.2f CCS \\n '%(I,I*36)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Traffic Intensity is 0.148 Erlangs = 5.33 CCS \n",
" \n"
]
}
],
"prompt_number": 11
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 2.6, Page 28"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Variable declaration\n",
"time=8.; #in hours\n",
"calls=11.; #no of calls in 90mins period\n",
"\n",
"#Calculations&Results\n",
"CR=calls/time; #call arrival rate in calls/hour\n",
"tavg=(3+10.+7+10+5+5+1+5+15+34+5)/11; #average call holding time in mins per call\n",
"I= CR*(tavg/60); #traffic intensity in Erlangs\n",
"print 'Traffic Intensity during eight hour period is %.3f Erlangs = %.1f CCS \\n'%(I,I*36);\n",
"\n",
"#For Busy Hour i.e between 4:00PM and 5:00PM\n",
"CRB=2; #call arrival rate during busy hour in calls/hour(from table 2.2)\n",
"tavgB=(34+5.)/2; #average holding time during Busy Hour in mins/call (from table 2.2)\n",
"IB=CRB*(tavgB/60); #Traffic Intensity during Busy Hour\n",
"print 'Traffic Intensity during busy hour is %.2f Erlangs = %.1f CCS'%(IB,IB*36);"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Traffic Intensity during eight hour period is 0.208 Erlangs = 7.5 CCS \n",
"\n",
"Traffic Intensity during busy hour is 0.65 Erlangs = 23.4 CCS\n"
]
}
],
"prompt_number": 14
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 2.7, Page 29"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Variable declaration\n",
"minutes=500.; #No of minutes used per month per user\n",
"Twork=0.9; #Traffic During Work day\n",
"TBH=0.1; #Traffic during busy hour\n",
"Days=20; #No of workdays in a month\n",
"\n",
"#Calculations\n",
"#Avg BH usage per subscriber (in minutes) = minutes*Twork(TBH/Days);\n",
"Traffic=minutes*Twork*(TBH/Days);\n",
"\n",
"#Result\n",
"print 'Traffic per user per BH is %.4f Erlangs \\n'%(Traffic/60);"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Traffic per user per BH is 0.0375 Erlangs \n",
"\n"
]
}
],
"prompt_number": 15
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 2.8, Page 29"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Variable declaration\n",
"minutes=500.; #No of minutes used per month per user\n",
"Twork=0.9; #Traffic During Work day\n",
"TBH=0.1; #Traffic during busy hour\n",
"Days=20; #No of workdays in a month\n",
"MeanHT=100; #Mean holding time(in secs)\n",
"\n",
"#Calculations\n",
"#Avg BH usage per subscriber (in minutes) = minutes*Twork(TBH/Days);\n",
"#BHCAs=traf\ufb01c (in Erlangs) *3600/(meanHT)\n",
"\n",
"Traffic=minutes*Twork*(TBH/Days);\n",
"BHCAs=(Traffic/60)*(3600/MeanHT);\n",
"\n",
"#Result\n",
"print 'Average Busy Hour call attempts are %.2f'%BHCAs"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Average Busy Hour call attempts are 1.35\n"
]
}
],
"prompt_number": 16
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 2.9, Page 35"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Variable declaration\n",
"Tpopu=200000;#Total population\n",
"SP=0.25; #subscriber penetration\n",
"HT1=100.; #holding time for Mobile to Land line and vicecersa\n",
"c1=3; #Avg calls/hr for Mobile to Land line and vicecersa\n",
"HT2=80.; #For mobile to mobile\n",
"c2=4; #For mobile to mobile\n",
"TMSC=1800; #traffic one msc can hold\n",
"TrafDist=0.9 #Traffic distribution for Mobile to Land line and vicecersa\n",
"\n",
"#Calculations\n",
"aM_L=c1*HT1/3600; #Traffic Generated by Subscriber (M-L and L-M).\n",
"aM_M=c2*HT2/3600; #Traffic Generated by Subscriber (M-M).\n",
"WlessSub=SP*Tpopu; #total wireless subscribers\n",
"TotalTraffic=WlessSub*TrafDist*aM_L+WlessSub*(1-TrafDist)*aM_M;\n",
"MSCreqd=TotalTraffic/TMSC;\n",
"if(MSCreqd-int(MSCreqd)>0):#for rounding of to next integer ef 2.33 to 3\n",
" MSCreqd=MSCreqd+1;\n",
" \n",
"\n",
"#Result\n",
"print 'Total Traffic is %.1f Erlangs'%TotalTraffic;\n",
"print 'NO of MSCs Required are %d'%(int(MSCreqd))"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Total Traffic is 4194.4 Erlangs\n",
"NO of MSCs Required are 3\n"
]
}
],
"prompt_number": 18
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 2.10, Page 37"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Variable declaration\n",
"Rlines=15000.;#Residential lines\n",
"Blines=80000.;#Business lines\n",
"PWElines=5000;#PBX, WATS, and Foreign Exchange (FX) lines\n",
"CR_R=2.;#Call rates for Rlines\n",
"CR_B=3.;# call rates for Blines\n",
"CR_PWE=10.;#call rates for PWElines\n",
"HT_R=140.;#average holding time for Rlines(sec)\n",
"HT_B=160.;#average holding time for Blines(sec)\n",
"HT_PWE=200.;#average holding time for PWE lines(sec)\n",
"Slines=100000.;# no of lines carried by switch\n",
"HD_ABS=1.5;# HD/ABS for the switch\n",
"\n",
"#Calculations\n",
"percentR_lines=Rlines/Slines;\n",
"percentB_lines=Blines/Slines;\n",
"percentPWE_lines=PWElines/Slines;\n",
"CCSR=CR_R*HT_R/100;\n",
"CCSB=CR_B*HT_B/100;\n",
"CCSPWE=CR_PWE*HT_PWE/100;\n",
"\n",
"CR=CR_R*percentR_lines+CR_B*percentB_lines+CR_PWE*percentPWE_lines;\n",
"print 'The call rate is %.1f calls per line \\n '%CR\n",
"CCS=CCSR*percentR_lines+CCSB*percentB_lines+CCSPWE*percentPWE_lines;\n",
"AvgHTperline=CCS*100/CR;\n",
"ABS_BH_calls=CR*Slines;\n",
"ABS_BH_usage=CCS/36*Slines;\n",
"print 'Design cell capacity based on HD is %d calls \\n'%(HD_ABS*ABS_BH_calls);\n",
"print 'DESIGN Erlangs based on HD is %d \\n'%(round(HD_ABS*ABS_BH_usage)); "
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The call rate is 3.2 calls per line \n",
" \n",
"Design cell capacity based on HD is 480000 calls \n",
"\n",
"DESIGN Erlangs based on HD is 21917 \n",
"\n"
]
}
],
"prompt_number": 23
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 2.11, Page 43"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Variable declaration\n",
"maxcalls_hour=4000.;#maximum call per hour\n",
"avgHT=160.;#average holding time in sec\n",
"Gos=0.02;\n",
"\n",
"#Calculations&Results\n",
"A=maxcalls_hour*avgHT/3600; #offered load\n",
"print 'Offered load A = %.2f Erlangs \\n'%A\n",
"#Refering Appendix A i.e Erlang B table \n",
"print \"For calculated Offered load and referring Erlang B table we get Service channels as 182 giving 168.3 Erlangs at 2% blocking\"\n",
"#Incorrect answer in textbook"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Offered load A = 177.78 Erlangs \n",
"\n",
"For calculated Offered load and referring Erlang B table we get Service channels as 182 giving 168.3 Erlangs at 2% blocking\n"
]
}
],
"prompt_number": 27
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 2.12, Page 43"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Variable declaration\n",
"channels=50;\n",
"blocking=0.02;\n",
"HT=120;#average holding time inm sec\n",
"BHcall=1.2;# in calls per hour\n",
"\n",
"#Calculations\n",
"#Refering Erlang B table in appendix A, For 50 channels at 2% blocking, the offered load=40.26 Erlangs.\n",
"A=40.26;\n",
"B=A*(1-0.02); #carried load\n",
"Avgtraffic_user=BHcall*HT/3600;\n",
"No_users=B/Avgtraffic_user;\n",
"\n",
"#Result\n",
"print 'NO of mobile subscribers supported are %d \\n'%(round(No_users))"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"NO of mobile subscribers supported are 986 \n",
"\n"
]
}
],
"prompt_number": 29
}
],
"metadata": {}
}
]
}