SCIENCE CHINA Information Sciences, Volume 60 , Issue 10 : 102304(2017) https://doi.org/10.1007/s11432-016-9012-7

Energy-efficient resource allocation for hybrid bursty services in multi-relay OFDM networks

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  • ReceivedDec 14, 2016
  • AcceptedJan 11, 2017
  • PublishedMay 19, 2017



The work was supported by National Nature Science Foundation of China Project (Grant No. 61471058), Hong Kong, Macao and Taiwan Science and Technology Cooperation Projects (Grant Nos. 2014DFT10320, 2016YFE0122900), Beijing Nova Program (Grant No. xx2012037), Shenzhen Science and Technology Project (Grant No. 20150082), and Beijing Training Project for the Leading Talents in S&T (Grant No. Z141101001514026).



Proof of the average performance equivalent

With the same data packet departure (that is homogeneous Poisson process), there are two kinds of data packet arrival, which are equivalent about the average performance, i.e., delay in this paper. The two types of data packet arrival can be described as follows.

Homogeneous Poisson arrival: The data packets arrive with a fixed rate $\lambda$ with a period of time $T$.

Heterogeneous Poisson arrival: The data packets arrive with a changed rate $\lambda(t)$ with regard to time $t$ within a period of time $T$, and the following constraint is satisfied, as given by \begin{equation} \lambda \cdot T = \int_0^T \lambda(t) \cdot {\rm d}t. \tag{39}\end{equation}

Since the departure process is identical, the equivalence of the two queue systems can be ensured if the equivalence of the two arrival processes can be proved within time duration $T$. Observing the whole queue system at time $T$, it is seen that the waiting time, depending on the state of queue system, will be same for different queue systems as long as the probability of queue length is identical. It is noted that only same average performance at time $T$ is guaranteed, but not the transient performance or any time before $T$.

As for homogeneous poisson arrival, the probability of arriving $k$ data packets within time $T$ can be expressed as \begin{equation} P_k^1(T)=\frac{(\lambda \cdot T)^k}{k!}{\rm e}^{-\lambda \cdot T}.\end{equation}

Similarly, for heterogeneous poisson arrival, this probability of arriving $k$ data packets can be obtained, as given by \begin{equation} P_k^2(T)=\frac{\left(\int_0^T\lambda(t) \cdot {\rm d}t\right)^k}{k!}{\rm e}^{-\int_0^T\lambda(t) \cdot {\rm d}t}.\end{equation} According to 39, $P_k^1(T)=P_k^2(T)$ is obtained which indicates that the probability of arriving $k$ data packets within time $T$ is identical. It is obvious that the probability of leaving $q$ data packets within time $T$ is identical too due to the same departure process, resulting in the same state of queue system. Therefore, it is proved that the two kinds of process are equivalent if the constraint 39 is satisfied.

The average time duration can be written as $T_1^s+\frac{1}{\Lambda_1^s}$ for service $s$ in downlink from a burst arrival to another burst arrival periodically. The burst data packet arrival is a heterogeneous poisson process, thus the following relationship can be obtained with the arrival rate $\lambda_1^s$ during bursty duration while $0$ during bursty interval, as given by \begin{equation} \int_0^{T_1^s+\frac{1}{\Lambda_1^s}} \lambda(t) \cdot {\rm d}t = \int_0^{T_1^s} \lambda_1^s \cdot {\rm d}t + \int_{T_1^s}^{T_1^s+\frac{1}{\Lambda_1^s}} 0 \cdot {\rm d}t=\lambda_1^s \cdot T_1^s.\end{equation}

Since ${\lambda_1^s}^*=\frac{\lambda_1^s~\cdot~T_1^s}{{T_1^s+\frac{1}{\Lambda_1^s}}}$, the new homogeneous poisson arrival with the parameter of ${\lambda_1^s}^*$ can meet the constraint 39 due to the following relationship, as given by \begin{equation} {\lambda_1^s}^*\left({T_1^s+\frac{1}{\Lambda_1^s}}\right)= \lambda_1^s \cdot T_1^s =\int_0^{T_1^s+\frac{1}{\Lambda_1^s}} \lambda(t) \cdot {\rm d}t.\end{equation}

Therefore, it is completely proved that it is equivalent on average performance for the bursty arrival and the homogeneous poisson arrival with the parameter of ${\lambda_1^s}^*$.


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  • Figure 1

    (Color online) Hybrid bursty services transmission in TWMR OFDM networks.

  • Figure 2

    (Color online) Bursty traffic of single service.


    Algorithm 1 The mapped two-way water filling allocation

    Require:Chromosome number in ESGA: Popsize, iteration number in ESGA: $g_c$, service number: $S$, channel conditions: $\{h_m^n,~g_m^n\}$, QoS requirements, and bursty traffic features;

    Obtain sum-rate constraints from the QoS requirements through equivalent queue analysis for all services;

    According to the integrated-noise-channel selection criterion, the optimal relay for each subcarrier is selected and the optimal channel conditions are recorded;

    Calculate the comprehensive two-way channel coefficients for each subcarrier;

    for $i=1:$ Popsize

    Initialize the subcarrier assignment sequence satisfying the $\{C_s^n\}$ constraints of each service for chromosome $i$;

    end for

    for $g=1:g_c$

    for $i=1:$ Popsize

    for $j=1:S$

    Resolve water level according to 33 for service $j$;

    Conduct the rate allocation and obtain the data rate ${r_1}$ and ${r_2}$ according to water level for service $j$;

    if $\forall~{r_1}~<~0$, $\forall~{r_2}~<~0$ then

    Let these negative data rates be 0 and exclude these subcarriers. Turn to Step Cal_water;

    end if

    end for

    Calculate the fitness according to the equivalent optimization function (37) as evaluating indicator;

    end for

    Select and record the best assignment scheme;

    Obtain the next generation by crossover and mutation;

    end for


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