1. Applied Mathematics and Communications Institute
Performance Analysis of Mixture of Unicast and Multicast Sessions in 5G NR Systems
Andrey Samuylov, Dmitri Moltchanov, Alesia Krupko, Roman Kovalchukov,
Faina Moskaleva, and Yuliya Gaidamaka
Applied Mathematics and Communications Institute

2. Outline Features of mmWave in 3GPP New Radio (NR) air interface
System model for 3GPP NR multicasting
Mathematical model as a queuing system with combination of unicast and multicast traffic
Numerical analysis

3. SYSTEM MODEL FOR 3GPP NR MULTICASTING
Network Deployment (1/2)
System:
NR access point (AP) with unicast and multicast sessions
Features:
propagation specifics of mmWave band
linear antenna arrays at both AP and UE
random resource requirements induced by locations of UEs
human blockage phenomenon
Fig. 1. Coexistence of sessions at a single NR AP

4. SYSTEM MODEL FOR 3GPP NR MULTICASTING
Network Deployment (2/2)
Metrics:
unicast session drop probability
multicast session drop probability
system resource utilization
Goal:
determine optimal AP intersite distance for 3GPP NR systems
Fig. 1. Coexistence of sessions at a single NR AP

5. Outline Features of mmWave in 3GPP New Radio (NR) air interface
System model for 3GPP NR multicasting
Assumptions
Multicast sessions: “transparent” service
CDFs for unicast and multicast random resources requirements
Propagation, Blockage and Antenna Models
Mathematical model as a queuing system with combination of unicast and multicast traffic
Numerical analysis

6. SYSTEM MODEL FOR 3GPP NR MULTICASTING
Assumptions
Single AP:
rA - radius of the coverage area of NR AP
Coexistence of unicast and multicast traffic:
BM - amount of resources for a multicast session, random variable (RV)
BU - amount of resources for a unicast session, RV
Unicast session:
“traditional” service - the amount BU of resources should be allocated for each new session
Multicast session:
“transparent” service

7. SYSTEM MODEL FOR 3GPP NR MLTICASTING
Multicast sessions: “transparent” service

8. SYSTEM MODEL FOR 3GPP NR MULTICASTING
CDFs for random resources requirements
Unicast session:
Suppose RV BU=const=d.
Multicast session:
𝑏1<𝑏2<…𝑏𝐾 – the values of RV BM
with CDF Pr⁡{ 𝐵 𝑀 =𝑏𝑘}=ф𝑘, 𝑘=1,…,𝐾,
ф𝑘 - the probability that multicast session requires 𝑏𝑘 resources, 𝑘=1,…,𝐾

9. SYSTEM MODEL FOR 3GPP NR MULTICASTING
Propagation, Blockage and Antenna Models
hA – height of AP
hU – height of UEs
hB – height of cylindrical blocker
rB – radius of cylindrical blocker
λB – intensity of spatial Poisson process
Fig. 2. LoS blockage zone

10. Outline Features of mmWave in 3GPP New Radio (NR) air interface
System model for 3GPP NR multicasting
Mathematical model as a queuing system with combination of unicast and multicast traffic
Queuing model
AP Characterizations
AP Resource Request Distribution
Numerical analysis

11. SYSTEM MODEL FOR 3GPP NR MULTICASTING
Queuing model: parameters
Fig. 3. Queuing system with combination of unicast and multicast traffic.

12. SYSTEM MODEL FOR 3GPP NR MULTICASTING
Queuing model: Markov chain (1/2)
𝐶 - amount of resources in the system
𝑑 - resources demand for unicast sessions
𝑏1<𝑏2<…𝑏𝐾 – resources demands for multicast sessions
𝑛(𝑡) – number of unicast sessions in the system at time t
𝑟(𝑡) – total amount of resources occupied in the system at time t
𝑟(𝑡)= 𝑈 𝑈 (𝑡)+ 𝑈 𝑀 (𝑡)
(𝑛(𝑡), 𝑟(𝑡)) - state of the system at time t
(2)
Mathematical model:
𝑛 𝑡 ,𝑟 𝑡 , 𝑡>0 – Markov chain
𝑋= 𝑛,𝑟 :0≤𝑛≤ 𝐶 𝑑 ,0≤𝑟≤𝐶 - set of states

13. SYSTEM MODEL FOR 3GPP NR MULTICASTING
Queuing model: Markov chain (2/2)
Fig. 4. Markov chain state transition diagram.

14. Queuing model: performance metrics
Mean amount of occupied resources in the system:
(7)
Set of unicast session drop states:
(8)
Unicast session drop probability:
(9)
Set of multicast session drop states:
(10)
(11)
Multicast session drop probability:

15. AP Coverage Characterizations
Smin - minimum SNR a system may tolerate
γ - path loss exponent
hA and hU - heights of AP and UE
PT - AP transmit power
GT and GR - AP transmit and UE receive antenna gains, respectively
N0 - thermal noise at receiver
LB=15 dB - blockage-induced losses,
A - constant in the path loss model 𝐴 𝑟 −𝛾
To find AP coverage: 𝑆 𝑚𝑖𝑛 = 𝐶 𝐵 ( 𝑟 𝐴 + [ ℎ 𝐴 − ℎ 𝑈 ] 2 ) −𝛾/2 ,
Solving (12) we arrive to 𝑟 𝐴 = ( 𝐶 𝐵 / 𝑆 𝑚𝑖𝑛 ) 𝛾/2 + ( ℎ 𝐴 − ℎ 𝑈 ) 2
(12)
(13)

16. AP Resource Request Characterizations
CDF of the distance between UE and AP
𝐹 𝐷 𝑦 = 𝑦 2 − ℎ 𝐴 − ℎ 𝑈 𝑟 𝐴 2 ,
The distribution of SNR SnB in non-Blocking conditions:
𝐹 𝑆 𝑛𝐵 𝑦 =1− 𝐹 𝐷 ( 𝛾 𝐶 𝑛𝐵 /𝑦 ),
The distribution of SNR SB in Blocking conditions:
𝐹 𝑆 𝐵 𝑦 =1− 𝐹 𝐷 ( 𝛾 𝐶 𝐵 /𝑦 ),
Blockage probability at the distance x [10]:
𝑝 𝐵 𝑥 =1− 𝑒 −2 𝜆 𝐵 𝑟 𝐵 𝑥 ℎ 𝐵 − ℎ 𝑈 ℎ 𝐴 − ℎ 𝑈 + 𝑟 𝐵 .
(14)
(15)
(16)
(17)

17. фk = 𝑃𝑟 𝑠 𝑘 ≤𝑆< 𝑠 𝑘+1 =𝐹 𝑆 𝑠 𝑘+1 − 𝐹 𝑆 𝑠 𝑘 .
AP Resource Request Distribution
With obtained CDFs 𝐹 𝑆 𝑛𝐵 𝑦 , 𝐹 𝑆 𝐵 𝑦 , 𝑝 𝐵 𝑥 we get CDF for SNR 𝑆
𝐹 𝑆 𝑦 = 1− 𝑝 𝐵 𝐹 𝑆 𝑛𝐵 𝑦 + 𝑝 𝐵 𝐹 𝑆 𝐵 𝑦 ,
where 𝑝 𝐵 = 0 𝑟 𝐴 𝑝 𝐵 𝑥 𝑑𝑥 .
(18)
With given SNR margins 𝑠1<𝑠2<…<𝑠𝐾 for 𝐾 different MCS schemes we obtain resource request distribution
фk = 𝑃𝑟 𝑠 𝑘 ≤𝑆< 𝑠 𝑘+1 =𝐹 𝑆 𝑠 𝑘+1 − 𝐹 𝑆 𝑠 𝑘 .
(19)

18. Outline Features of mmWave in 3GPP New Radio (NR) air interface
System model for 3GPP NR multicasting
Mathematical model as a queuing system with combination of unicast and multicast traffic
Numerical analysis

19. Drop probabilities vs sessions arrival intensities

20. Drop probabilities vs sessions service intensities

21. System resource utilization vs sessions arrival intensities

22. Conclusions
The model of the service process at NR AP is served a mixture of unicast and multicast traffic that takes into account
propagation specifics of a mmWave band,
linear antenna arrays at both AP and UEs
stochastic locations of users
The increase in multicast session arrival rate and/or mean service time results in a decrease of the multicast session drop probability.
The proposed model can be used for dimensioning of prospective NR systems.

23. Thank you! Faina Moskaleva Tel.: +7 916 955 72 00