The service process of sessions in 3GPP New Radio (NR) wireless access systems operating in millimeter wave frequency band is heavily afected by the dynamic blockage of propagation paths between user equipment (UE) and access point (AP). Although the ability of UEs' transievers to operate over reflected propagation path components partially compensates for this phenomenon, it simultaneously leads to the dynamic fluctuations in the amount of resources requested during the session lifetime to support the required bitrate. In our study, we formulate an accurate model of the 3GPP NR AP service process by taking into account time-varying changes in the amount of requested resources caused by dynamic blockage of propagation paths. The derived metrics of interest includes new and ongoing session drop probabilities as well as the system resource utilization. The presented numerical results indicate that the presence of blockage events decreases the probability of session drops upon arrival at the expense of increasing blocking probability during the service process. However, it does not drastically afect the system resource utilization.
In December 2017 3GPP has rectified the Phase 1 LTE-anchored New Radio (NR) access technology. As the 3GPP eforts will now continue towards stand alone NR technology the emphasis of the research community is shifting towards the eficient use of the newly standardized system.
Performance of the mmWave deployments has been recently assessed using the tools
of stochastic geometry. Applying the Campbell theorem for functionals over point
processes, the moments of aggregate interference in THz and mmWave systems in
presence of molecular absorption, human-body blockage, and directional transmit and
receive antennas have been derived in [1]. Using the Taylor expansion approximation,
the authors then extended their analysis to the moments of signal-to-interference ratio
(SIR) in [2]. Particularly, the authors in [
The stochastic geometry approach allows to characterize wireless specifics of mmWave
communications leaving the question of trafic dynamics in mmWave access networks
unanswered. Acknowledging this problem, studies addressing both stochastic
components started to appear recently, see, e.g., [
In this paper, we use the tools of queuing theory to develop an accurate model of the session service process at a 3GPP NR access point (AP). To capture random locations of UE in the service area, the resource requirements are assumed to be random variable. Futhermore, to account for blockage of propagation paths between AP and UE we assume that there is external process of blockage. The target metrics of interest are new and ongoing sessions drop probabilities as well as the system resource utilization. 2.
We consider a single 3GPP NR AP. The amount of resources available at AP is
Hz. Consider a multiserver queuing system with servers, where arriving sessions
require a server and random amount of resources of total volume . The session arrival
process is homogenous Poisson with intensity . Each session, upon arrival, requeres
radnom amount of resources from the system, , with cumulative distribution function
(CDF) (). The random nature of resource requests stems from random locations
of UE in the AP service zone. Given a certain session rate, the set of modulation and
coding schemes (MCS) for 3GPP NR available in 3GPP Relese 15, 3GPP multipath
propagation model, and distribution of users in the AP service zone CDF () can be
found using conventional methods of stochastic geometry [
We use the standardized 3GPP stochastic multipath propagation model specified
in [
Access point User equipment Active link (LoS non-blocked) Active link (LoS blocked) r
x1 rB
x4 rB rB rB a rB ~ a2 users a rB xN2
Radio resources
rB
sessions R
xN xi rB x j rB 1 . . .
N
According to the abovementioned discussion each active session in the system is associated with a homogeneous Poisson process of events with intensity .1 Upon each event the active session changes its resource requirements by drawing them from the CDF (). If the new resource requirements is smaller, the session continues service at AP. alternatively, if the new resource requirements are higher the session might be dropped if there is insuficient amount of free resources at the AP current. Thus, in the considered system, a session can be dropped upon arrival or during the service process. We are interested in drop probabilities and new and already accepted sessions as well as in system resource utilization. 1In what follows, these events are referred to as “signals”.
For the analysis of the described queuing system we use the simplified approach, which is common for the queues with random resource requirements. Particularly, instead of keeping track of the amount of resources occupied by each session we track only total amount of resources occupied by all the sessions in the system.
allows to significantly reduce the complexity of the analysis, in the simplified system we do not know the exact number of resources that should be released at the departure time instant of a session or at the arrival time instant of a signal.
shortcoming and decide upon the amount ot resources released we use the Bayes law. Particularly, if sessions in the system occupy resources, then the probability that resources are released on the departure time instant is − probability that sessions occupy resources. The sought probability is estimated as (− 1)/(), where () is the () = ∑︁ − 1
(− ), ≥ 2.
Behavior of the system can be described by the stochastic process () = ( (), ()), where () denotes number of sessions in the system and () is the total amount of occupied resources. The set of states is provided in (2) =
⋃︁ 0≤ ≤ , = {︁
}︁ (, ) : 0 ≤ ≤ , () > 0 .
Arrange the states in in increasing order of the amount of the occupied resource and denote (, ) the sequence number of the state (, ). The stationary probabilities (3) of () are written as () = lim { () = , () = } , (, ) ∈ , (1) (2) (3) (4) where (1) = , ≥
0.
Resource reallocation at the arrival time instant of a signal is performed similarly, i.e., if sessions in the system occupy resources, then the probability that resources are (− 1)/(). Thus, after arrival of a signal sessions [(− − 1)/()](1 − fulfilled and it is lost. released upon signal arrival is − occupy resources with probability [(− − 1)/() ]− +, ≤ and with probability ∑︀− + ) new resource requirements of the session cannot be
=0 ︃( =0
)︃ ∑︁ 0(0) = ⎛ − ⎝
=0 + ( + 1)
∑︁ :(+1,+)∈+1 ∑︁ + + ⎠ () = − 1( − ) + +
∑︁ :(,)∈ + ( + 1) ()
∑︁
The system of equations (4) - (5) is complemented with the normalization conditions and then solved numerically. Since all state transitions take place between either states from one substate or states from adjacent substates and − 1, the generator matrix of () can be represented in block-tridiagonal form simplifying the solution.
Using the stationary probabilities, one can evaluate the main performance measures of the system: the average number of occupied resources in (5), session blocking probability (the probability that a session is lost upon arrival) in (6) and session blocking probability during the service time, (the probability that a session is dropped upon signal arrival) in (7): = 1 − =
(), ∑︁ (,)∈
∑︁ (,)∈,< () ∑︁ , − =0 =
∑︁ (,)∈ () ∑︁ (− − 1) ⎛
⎝1 − =0 () − + ∑︁ =0
⎞ ⎠ .
(5) (6) (7)
We specifically note that the ongoing session drop probability is interpreted as the fraction of signals that lead to the drop of ongoing session.
4.
In this section we provide sample illustrative results. The default system parameters used in what follows are provided in Table 1 below.
The response of the 3GPP NR system service process to input system parameters is illustrated in Figs. 3-6. Analyzing the behavior of the blocking probabilities upon arrival and during the service time as a function of the session arrival intensity one may observe that over the considered interval both curves are characterized by exponential behavior. Furthermore for the chosen value of system parameters the blocking probability upon session arrival is much higher than the blocking probability of session during the service time. To reveal the detailed behavior of these two metrics consider blocking probabilities upon arrival and during the session time as a function of signal intensity illustrated in Fig. 4. As one may observe, the increase in the signals intensity leads to the decrease in
The default system parameters.
Parameter Number of resource blocks per timeframe Number of servers available Sessions request distribution Mean session request size (RBs) Sessions arrival intensity Session service intensity
Value 100 100 geometric 2 the blocking probability of ongoing sessions. The probability that a session is blocked upon arrival decreases as well. The underlying reason for this behavior is that the increase in the signals intensity results in more sessions dropped during the service process due to insuficient amount of resources thus leaving more resources “on average” for new session arrivals. In extreme case when the signals intensities is very high, almost all the sessions are admitted in the system and then eventually dropped during the service process. Alternatively letting the signals intensity approaching zero no losses during the service time are experienced.
Fig. 5 shows the system resource utilization as a function of the signals intensity. As one may observe, for rather wide range of signals intensity the resource utilization remains almost the same. In spite of this behavior, more resources are wasted as signal intensity increases as more sessions leave the system prior to service completions. Thus, aside from classic systems, where system utilization is one of the critical performance indicators for systems provided in prospective 5G systems one has to consider more advanced metrics that quantify not only resource utilization but a fraction of resources wasted due to partial service.
Finally, Fig. 6 shows the new and ongoing session drop probability as a function of mean session size. Recall that keeping the session arrival rate constant while increasing the mean session size we increase the ofered trafic load to the size. Thus, expectedly, both probabilities are characterized by the increasing behavior. Similarly to previous illustrations the new session loss probability is higher than the ongoing session drop probability. 5.
In this paper we have developed an accurate model for the 3GPP NR system service process. The proposed models not only accounts for inherently variable session resource requirements induced by random rate requests and random location of users but captures the blockage of propagation path between UEs and AP. The latter is modeled by introducing an external process of events causing resource re-allocations for sessions already accepted to the system.
The developed model allows for systematic analysis of 3GPP NR AP service process in various deployments. The sample numerical results have shown that the presence of external process of signals modeling the blockage process decreases the probability of session drops upon arrival at the expense of increasing blocking probability during the service process. At the same time, it does not drastically afect the system resource utilization.
The publication has been prepared with the support of the “RUDN University Program 5-100” and funded by RFBR according to the research projects No.18-07-00576, 18-37-00380. This work has been developed within the framework of the COST Action CA15104, Inclusive Radio Communication Networks for 5G and beyond (IRACON).