The expected growth in the mobile video (including streaming video, video downloading, conferencing, etc.) now is the key driver for rapid development of 5G wireless network technologies. This paradigm forces wireless networks to manage their resources as efectively as possible. One of the most appropriate solutions for video trafic that may provide the suficient spectral eficiency is multicasting. Multicast sessions allows a group of users to simultaneously access the same multimedia content with the same QoE parameters. In this paper we consider diferent methods of multicast subgrouping. An analytical framework in the from of a queuing network is proposed to study the network performance, and a comparative study of network performance metrics under diferent user movement scenarios is presented.
According to [1], video will exceed the 82 percent of global Internet trafic by 2022. For network operators this leaves no other option but to strive for higher spectral eficiency as video data demands both high data rates and strict Quality of Experience (QoE) requirements. One of possible solutions is to employ the existing "enhanced" multimedia broadcast multicast services (e-MBMS) architecture [2], standardized by the Third Generation Partnership Project, by adopting it to the 5G systems. This will enable 5G networks with all the opportunities of the point-to-multipoint services which are crucial to support large-scale consumption of mass multimedia services on mobile devices [3].
In this paper we consider multicast approaches of network ofloading. In [4] an approach based on splitting users into multicast subgroups (subgrouping) was proposed. This approach allows to achieve better results in terms of considered metrics rather then allocating the whole pool of resources to a single multicast group. The author also propose an algorithm that allows to find a sub-optimal network configuration consisting of two sets (groups) of users and resources allocation scheme for them. The algorithm considers maximization of Aggregate Data Rate (ADR) metric, thus improving the overall throughput of the network. Due to its low complexity the algorithm satisfies computation timing constraints since it should be run every Time Transmission Interval (TTI) during which channel quality between a multicast user and the base station is considered to be constant and may be just 1 ms long. Besides, for distant users it is extremely important to take into account their spatial positions as the amount of utilized resource significantly varies [15], mainly due to the efect of interference [16, 17].
An analytical model for characterizing the impact of the users’ mobility in the multicast subgroup formation problem was proposed in [5] since queuing theory [7, 18] is typically employed in description of telecommunication networks . It is shown that, under the condition of constant number of multicast users within the service area, user mobility can be modeled as a queuing network. The model allows for close analytical calculation of average experienced bit rate and maximum aggregate data rate as an optimal solution of the subgroup formation problem stated in [4].
In this paper we study the range of applicability of the algorithm proposed in [4]. We also extend the model proposed in [5] to take into account the ’ON-OFF’ (active-passive) operation mode of user devices. As ADR metric is usually unfair towards end users we also consider other metrics that may be more appropriate in diferent scenarios. 2.
Each device in a multicast group transmits periodic or aperiodic feedback signals that allow base station (BS) to define Channel Quality Indicator (CQI). On collecting the state information from all the devices inside the coverage area, the BS makes a decision on subgrouping of these devices. As the time for taking a decision is limited by one Transmission Time Interval (TTI) an efective mechanism is required for resource allocation, which can operate within very short run time.
The simplest way to distribute multicast resources is to maintain equal data rate across all the devices. Among the many alternative solutions, the subgrouping method are given most of attention, as they can provide the highest throughput. Group-based methods consist of dividing a set of multicast objects into several subgroups consisting of receivers. Each subgroup is served with MCS that can be applied to the subgroup member with the worst channel conditions [12, 14]. Time-free and multi-layer coding techniques [6, 11] can be applied to subgroups to guarantee continuity and integrity of data transmission, and to eficiently handle subgrouping process.
The main problem in subgrouping is the computational complexity (and time) needed to find an optimal subgroup configuration (see Fig. 1). It is usually calculated using exhaustive search schemes. Run-time is critical in any wireless system where multicast objects can experience channel fluctuations during the time interval required by BS to form subgroups according to the collected CQIs.
2.1.
We refer to a single-cell coverage area with one multicast group, composed of set A = {1, · · · , } of members. The BS allocates RBs according to the Channel Quality Indicator (CQI) feedbacks [13]. Let M = {1, · · · , } be the set of available CQIs, be the number of members reported -CQI, = (1, · · · , ). Since each CQI is associated with supported MCS, we indicate with , ∈ M the data transmitted over one Resource Block (RB) by using the Modulation and Coding Scheme (MCS) corresponding to the -th CQI. The BS enables the subgroup configuration, i.e., the number of subgroups with their relevant MCS and amount of allocated resources that maximizes the ADR. Let us denote L = {1, · · · , }, L ∈ M the set of subgroups in the current moment, M = { ∈ M : > 0} the set of CQIs which are reported by at least one user, and ∈ L, ∈ M the afiliation of -th CQI to -th subgroup. Reported CQIs are divided into existing subgroups. Let represent the number of resource blocks allocated to -th subgroup, k = (1, · · · , ) 2.2.
The number of members and the values of CQIs reported by each member. Nevertheless, if we would like to know the situation not only at the current moment but also predict it in the future we could add stochastic nature in the problem formulation. In this paper we analyze the scenario of users that are moving within the circular cell of radius . The directions the users are moving are learned from statistics of event-based simulation to find the probability that a user will change the area of the some MCS within a timeslot [5, 10]. A circular cell is divided in disjoint areas of the same CQI. We assume free space, so the areas have forms of annulus. Users are distributed according to a Poisson Point Process (PPP) on the plane and thus are uniformly deployed within a cell. Let us denote ,− 1 the probability of events when a user moves farther from the BS and changes the reported CQI from to − 1; ,+1 = 1 − ,− 1 the probability of events when a user moves closer to the BS and changes the reported CQI from to + 1; and the average time when a user does not move from the area of -MCS, i.e. he does not change its CQI from . 3.
In this section we first present a queuing network, where each node describes the channel quality level ∈ M, where M is the set of all channel quality indicators (CQIs). The considered network is closed, i.e. it is a network with a set of nodes without source and drain, in which a constant number of similar arrivals are circulating [9]. 3.1.
Earlier in [5] the queuing network was considered only with "active" users, that is,
the subscribers which use the mobile network continuously. The transition digram for
the considered queuing network is schematically presented in Fig. 2.
The state space of the system (M, ) satisfies the relation (
(
In this case, the stationary probabilities () of the states of the system are calculated
as (
() = − 1(M, ) ∏︁ (ℎ) .
!
=1
(ℎ)
!
as (
where (M, ) = ∑︀∈(M,) ∏︀
=1 ⎪ ⎩ ℎ = ℎ− 1 − 1.
ℎ = ℎ− 1 − 1 + ℎ+1(1 − +1), 2 ≤ ≤ − 1; 3.2.
Similarly, we may describe the model for devices operating in two modes (the ’ONOFF’ model), where the 0-node describes the ’passive’ (or ’OFF’) mode, when devices do not exchange the data with the BS (Fig. 3).
Here passive node is denoted as 0-node, and is the total number of customers in
the system in both active and passive nodes. , = 1, indicate the probabilities of
transitions of active users between adjacent nodes, while 0, where = 1, , indicate
the probabilities of transitions from the passive node to the active ones. The average
time until the user moves from the area is similarly indicated with . In order to
prove that a given physical system exists, we show that passive node is in one of the
available states, that is, satisfies the normalization condition (
=1
The state space of the system (M, ) satisfies the relations (
In this case, the stationary probabilities () of the states of the system are calculated
as (
⎧ ⎪ ℎ1 = ℎ2 21 + ℎ0 01; ⎨ ⎪ ⎩ ℎ = ℎ− 1 − 1 + ℎ0 0 .
ℎ = ℎ− 1 − 1 + ℎ+1 +1 + ℎ0 0− 1, 2 ≤ ≤ − 1; users 4.
The problem of calculating the subgroup configuration for a wireless multicast network can be considered in the context of two possible scenarios: in the first scenario, the total data rate is found in order to achieve maximum throughput of the whole network. In the second scenario, the rates are somehow evenly distributed among all devices. In this section, the main goal for scenario 1 is to analyze the range of applicability of the algorithm proposed in [4], while for the second scenario is to study the fairness of resource distribution between devices by the Jain’s fairness index [8] for the considered utility functions.
4.1.
Aggregate Data Rate shows the overall size of data that can be downloaded within one TTI by the devices what is extremely important for applications that involve on-line video streaming and thus require higher throughput.
To calculate the Aggregate Data Rate we use an objective function (
= ∑︁ (︁ =1
(︀ = {M1, · · · , M}, = (1, · · · , )︀) = min∈M () · ·
︁)
∑︁ := → .
∈M
(
In Fig. 4 relative diference of results obtained with use of the considered algorithm and brute force analysis is shown.
The results include 3 possible scenarios: uniform,
centered and boundary trend of users’ disposition.
(
FDR tries to minimize diference in average rates (
︁) 1≤ ≤ min ︁( min∈M () · := → .
︁)
BDR maximizes the minimal rate without taking into account higher rates (
︁)
PF maximizes the total network bandwidth and evenly distribute the rates (
︂) ∑︁ := → . ∈M
Input data for numerical experiment Parameter Uniform Centered Boundary
Value
15
50
16
(
For input data presented in Table 1 we present numerical results (Table 2). The obtained results show that in case of uniform and centered distribution of users over the service area, the FDR function allows to find the finest network configuration. But in case the users are distributed mainly by the cell’s boundaries, it is much more efective to use PF function. If users behave in the way that they are always either closer to the center or to boundaries, the preferred decision should be to select BDR function. 5.
In this paper we considered diferent methods of multicast subgrouping. We introduced an analytical model for multicast-enabled network cell that includes user mobility and in-of operation modes.
We also provided the numerical analysis of the range of applicability for the ADR
maximization algorithm. Finally, we presented three objective functions that allow for data rate equalization among users with diferent channel quality conditions, and provided the numerical analysis based on Jane’s fairness index to reveal the scenarios that are applicable for the functions.
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. 18-0001555(18-00-01685) and No. 18-37-00231.