Adaptive Carrier Aggregation with Differentiating Cloud Services for Maximizing Radio Resource Efficiency and Reward Toward 5G Cellular Network

Abstract

Toward 5G cellular network, to achieve an extremely high data rate and Ultra Reliable Low Latency Communication by using a limited radio frequency spectrum bands becomes a big challenge. 3GPP LTE-A/LTE-A Pro thus specifies the technologies of Carrier Aggregation (CA) and Network Function Virtualization (NFV) to increase the frequency spectrum efficiency and to dynamically allocate the virtualized network component for different classes of requests, respectively. CA can aggregate multiple contiguous or non-contiguous Component Carriers (CCs) and to improve frequency spectrum utilization and signal quality. NFV can dynamically allocate network (virtualized) resource for different classes of services, e.g., human-driven Cloud Computing, machine-driven Internet of Vehicles (IoVs) (e.g., Autonomous Self Driving Vehicle) and sensing-based Internet of Things (IoTs), etc. However, different SINRs of different frequency spectrum bands suffer from the exiting radio nature of CCs. The CA effect and system capacity are thus limited obviously. Additionally, in CC accesses via IoV/IoT, human-driven and machine-driven types communications exhibit different arrival requests and traffic characteristics. Various QoS requirements and traffic distributions of Human and Machine transmissions are certainly different. This paper thus proposes the Cross-Layer scheduling with CC Aggregation (CLCA) toward 5G. CLCA consists of three mechanisms: (1) Markov Decision Process-based cost reward Packet Selection (MDP-PS), (2) Adaptive Packet Scheduling (APS) and (3) Adaptive Component Carrier scheduling (ACC). Numerical results demonstrate that the proposed CLCA approach outperform the compared approaches in system capacity, network reward and packet failure rate.

Appendix

The proof of Theorem 3.1 is depicted in detail in this appendix.

Initially, a stochastic process of the usage of the radio Resource Block (RB) $\{ X_{t} :t \in T\}$ is defined to establish a RB Continuous-Time Discrete-State Markov Chain (namely CTMC) model if for any time $t_{i} \in R_{0}^{ + }$, with $0 = t_{0} < t_{1} \cdots < t_{n} < t_{n + 1}$,$\forall n \in N$, and the RB state $\forall s_{i} \in S = N_{0}$ for the probability mass function (pmf). The exponential distribution is the only Continuous-Time distribution that provides the memoryless property, the state sojourn times of the CTMC model are necessary exponentially distributed. Assume that the state sojourn time of the RB usage-events in the model is exponentially distributed, and thus has the following relation,

$$P[X_{{t_{n + 1} }} = s_{n + 1} |X_{{t_{n} }} = s_{n} , \ldots ,X_{{t_{0} }} = s_{0} ] = P[X_{{t_{n + 1} }} = s_{n + 1} |X_{{t_{n} }} = s_{n} ].$$

(25)

That is, the proposed MDP-based RB usage model has the memoryless property. This implies that the current RB state only depends on the last RB state. That is, the RB usage model has the homogeneity property. The continuous-time transition probability from state $i$ to state $j$ during the period $[e,f)$ then can be expressed by

$$p_{ij} (e,f) = P[X_{f} = j|X_{e} = i],$$

(26)

where $e,f \in T{\text{ and }}e \le f$. The Chapman–Kolmogorov equation [45] for the transition probabilities of Eq. (25) of the RB CTMC is then derived by

$$p_{ij} (e,f) = \sum\limits_{k \in S} {p_{ik} (e,g)} \cdot p_{kj} (g,f),$$

(27)

where $0 \le e \le g < f$.

Second, in Table 1, the change of RB states, $i \in S$, could be increased or decreased as the number of the allocated RBs is increased or decreased, respectively. That is, the birth–death process is essentially transited among states when the birth and death events arrive at the model. All the RB-states, $i \in S$, in the model can be reached from any other RB-states, $j \in S,j \ne i$. Any RB state is not an absorbing state, i.e., $p_{ii} = 1$. This represents that the homogeneous model is irreducible and has the initial-state independent property, i.e.,

$$\mathop {\lim }\limits_{t \to \infty } p_{ij} (t) = \pi_{j} ,$$

(28)

or

$$\mathop {\lim }\limits_{t \to \infty } \pi_{j} (t) = \pi_{j} .$$

(29)

By applying Eqs. (28)–(29) to Eq. (27), the state probability at time $f$ is formulated as

$$\pi_{j} (f) = \sum\limits_{i \in S} {p_{ij} (e,f) \cdot \pi_{j} (e)} .$$

(30)

Therefore, the state probability vector, $\pi = [\pi_{0} ,\pi_{1} , \ldots ]$, at any instant time $f$ can be expressed by

$$\pi (f) = \pi (e) \cdot {\text{P}}(e,f),$$

(31)

where ${\text{P}}(e,f)$ is the transition probability matrix for any pair of RB states $i$ and $j$ at any time $[e,f)$, $e,f \in T{\text{ and }}e \le f$. The vector of the RB state probability is denoted by $\pi = [\pi_{0} ,\pi_{1} , \ldots ]$, in which the sum of the state probability is one, i.e., $\sum\nolimits_{j} {\pi_{j} = 1}$.

Third, the eNB’s RB state, $i$, is determined based on the number of allocated RBs for the incoming connections. Because the requested bandwidth and the CQI of an UE could be increased and decreased, all the requested bandwidth and their CQIs are independently and aperiodically. This breaks the periodical characteristic. Since a state $i$ of the irreducible homogeneous RB CTMC model is aperiodical, the other states $j \in S$ are aperiodical. Consequently, all the RB-states of the RB CTMC model are all aperiodical. Based on the aperiodical transition among RB-states, the transition rate $q_{ij} (t)$ of the RB CTMC model from state $i$ to state $j$ is derived from the related the continuous-time transition probability [45] as

$$q_{ij} (t) = \mathop {\lim }\limits_{\Delta t \to 0} \frac{{p_{ij} (t,t + \Delta t)}}{\Delta t}$$

(32)

and

$$q_{ii} (t) = \mathop {\lim }\limits_{\Delta t \to 0} \frac{{p_{ii} (t,t + \Delta t) - 1}}{\Delta t},$$

(33)

where $i \ne j$ and $\sum\limits_{j \in S} {q_{ij} (t)} = 0,\forall i \in S$. The total rate at which the RB model leaves state $i$ must equal the total rate at which the model enters state $i$. The infinitesimal generator matrix ${\text{Q}}$ of the transition probability matrix ${\text{P}} = [p_{ij} (0,t)] = [p_{ij} (t)]$ is defined as ${\text{Q}} = [q_{ij} ]$. After applying Eq. (32) to Eq. (31), we have the differential equation

$$\frac{d\pi (t)}{dt} = \pi (t) \cdot \text{P}^{\prime } (t) = \pi (t) \cdot {\text{Q}}(t).$$

(34)

Since the RB CTMC is time-homogeneous, we neglect the dependence upon time and then obtain

$$\frac{d\pi (t)}{dt} = \pi (t) \cdot {\text{Q}} .$$

(35)

The steady RB-state probabilities are independent of time, and then we have $\mathop {\lim }\limits_{t \to \infty } \frac{d\pi (t)}{dt} = 0$. Consequently, the differential equation of Eq. (35) for solving the steady trust-state probabilities is simplified by the system of linear equations

$$\pi \cdot {\text{Q = 0,}}$$

(36)

i.e.,

$$\pi_{j} \cdot q_{j} = \sum\limits_{j \ne i} {\pi_{i} \cdot q_{ij} } , \, \forall i,j \in S,$$

(37)

and

$$\sum\limits_{j} {\pi_{j} } = 1,$$

(38)

where $q_{j}$ is the transition rate out of RB state $j$ and $q_{ij}$ is the transition rate from RB state $i$ to RB state $j$.

Thus, the proposed MDP-based RB model of the birth–death process satisfies the required properties of the steady-state probability vector, i.e., time-homogeneous, irreducible and aperiodical. The Theorem 3.1 is thus proved.