Delay sensitive resource allocation over high speed IEEE802.11 wireless LANs

Abstract

We present a novel resource allocation framework based on frame aggregation for providing a statistical Quality of Service (QoS) guarantee in high speed IEEE802.11 Wireless Local Area Networks. Considering link quality fluctuations through the concept of effective capacity, we formulate an optimization problem for resource allocation with QoS guarantees, which are expressed in terms of target delay bound and delay violation probability. Our objective is to have the access point schedule down-links at minimum resource usage, i.e., total time allowance, while their QoS is satisfied. For implementation simplicity, we then consider a surrogate optimization problem based on a few accurate queuing model approximations. We propose a novel metric that qualitatively captures the surplus resource provisioning for a particular statistical delay guarantee, and using this metric, we devise a simple-to-implement Proportional–Integral–Derivative (PID) controller achieving the optimal frame aggregation size according to the time allowance. The proposed PID algorithm independently adapts the amount of time allowance for each link, and it is implemented only at the Access Point without requiring any changes to the IEEE802.11 Medium Access Control layer. More importantly, our resource allocation algorithm does not consider any channel state information, as it only makes use of queue level information, such as the average queue length and link utilization. Via NS-3 simulations as well as real test-bed experiments with the implementation of the algorithm over commodity IEEE 802.11 devices, we demonstrate that the proposed scheme outperforms the Earliest Deadline First (EDF) scheduling with maximum aggregation size and pure deadline-based schemes, both in terms of the maximum number of stations and channel efficiency by 10–30%. These results are also verified with analytical results, which we have obtained from a queuing model based approximation of the system. Applying actual video traffic from HD MPEG4 streams in both simulations and real test-bed experiments, we also show that our proposed algorithm improves the quality of video streaming over a wireless LAN, and it outperforms EDF and deadline based schemes in terms of the video metric, Peak Signal to Noise Ratio.

Appendices

Appendix

M/G/1 derivations

Recall that the packet service time $T_l$ is a discrete random variable with the following probability mass function (pmf):

$$\begin{aligned} {\mathsf {Pr}}\left( T_l = \frac{M.BI}{r_k\tau _l}\right) = \pi _{lk}, \end{aligned}$$

(20)

where M is the packet size in bits. The cumulative distribution function (CDF) of $T_l$ denoted by $B_l(t)$ then becomes,

$$\begin{aligned} B_l(t) = {\mathsf {Pr}}(T_l \le t) = 1-{\mathsf {Pr}}\left( r_k< \frac{M \cdot BI}{t\tau _l}\right) \nonumber \\ = 1 - \sum _{k=1}^{K} 1_{\left\{ r_k < \frac{M \cdot BI}{t\tau _l}\right\} } \pi _{lk}. \end{aligned}$$

(21)

where $1_{\{.\}}$ is the indicator function, which is 1 when its argument is true and 0 when its argument is false.

Approximating the system as an M/G/1 queue, the CDF of the residual service time is obtained as

$$\begin{aligned} \Psi _l (t) = {\mathsf {Pr}}(S_l \le t) = \mu _l \int _{0}^{t} \left( 1-B_l(x)\right) dx. \end{aligned}$$

(22)

Here, $\mu _l=\frac{1}{{\mathsf {E}}[T_l]}$ is the average packet service rate of link l, which can be easily obtained as,

$$\begin{aligned} \mu _l = \frac{\tau _l}{M \cdot BI} \sum _k \pi _{lk}r_k. \end{aligned}$$

(23)

Using (21) in (22) we obtain,

$$\begin{aligned} \Psi _l (t;\tau _l) = \mu _l \int _0^t \sum _k 1_{\{ \tau _l < \frac{M \cdot BI}{x r_k}\}}\pi _{lk} dx, \end{aligned}$$

(24)

where we have included the TXOP allocation $\tau _l$ as a parameter of the residual time CDF. By making a change in variable of $u=\frac{M \cdot BI}{x r_k}$, we obtain the following integral

$$\begin{aligned} \Psi _l (t;\tau _l) = - \mu _l \int _{u=\infty }^{\frac{M \cdot BI}{t r_k}} M \cdot BI \left( \sum _k 1_{\{ \tau _l< u\}}\frac{\pi _{lk}}{r_k}\right) \frac{du}{u^2} \nonumber \\ = \mu _l M \cdot BI \sum _k \frac{1}{r_k} \left( \int _{u=\frac{M \cdot BI}{t r_k}}^{\infty } 1_{\{ \tau _l < u \}}\pi _{lk} \frac{du}{u^2} \right) . \end{aligned}$$

(25)

Given the range of the integral and the indicator function condition, the following cases occur:

$$\begin{aligned} \int _{u=\frac{M \cdot BI}{t r_k}}^{\infty } 1_{\{ \tau _l< u \}}\pi _{lk} \frac{du}{u^2} = \left\{ \begin{array}{ll} \int _{u=\frac{M \cdot BI}{t r_k}}^{\infty } 1 \cdot \pi _{lk} \frac{du}{u^2}, & \quad \tau _l < \frac{M \cdot BI}{t r_k}; \\ \int _{u=\tau _l}^{\infty } 1 \cdot \pi _{lk} \frac{du}{u^2}, & \quad \tau _l \ge \frac{M \cdot BI}{t r_k}; \end{array} \right. \end{aligned}$$

(26)

In terms of the channel rate, $r_k$, the breakpoint can be obtained as:

$$\begin{aligned} r_k < \frac{M \cdot BI}{t \tau _l}. \end{aligned}$$

(27)

For convenience, let us define $K_l(t;\tau _l)$ as the index of the largest channel rate for which (27) holds for a given TXOP allocation $\tau _l$, i.e.,

$$\begin{aligned} K_l(t;\tau _l) = \sup _k \left\{ k|r_k < \frac{M \cdot BI}{t \tau _l} \right\} \end{aligned}$$

(28)

Applying (26)–(25) and splitting the summation on $K_l$ yields:

$$\begin{aligned}&\Psi _l(t;\tau _l) = \mu _l M \cdot BI \left( \sum _{k=1}^{K_l(t;\tau _l)} \pi _{lk}/r_k \int _{u=\frac{M \cdot BI}{t r_k}}^{\infty } du/u^2 + \right. \nonumber \\&\left. \sum _{k=K_l(t;\tau _l)+1}^{K} \pi _{lk}/r_k \int _{u=\tau _l}^{\infty } du/u^2\right) \nonumber \\&= \mu _l \left( t \sum _{k=1}^{K_l(t;\tau _l)} \pi _{lk} + \frac{M \cdot BI}{\tau _l} \sum _{k=K_l(t;\tau _l)+1}^{K} \frac{\pi _{lk}}{r_k} \right) . \end{aligned}$$

(29)

Substituting $\mu _l$ from (23), we obtain

$$\begin{aligned} \Psi _l(t;\tau _l) = \bar{r_l} \left( \frac{t \tau _l}{M \cdot BI} \sum _{k=1}^{K_l(t;\tau _l)} \pi _{lk} + \sum _{k=K_l(t;\tau _l)+1}^{K} \frac{\pi _{lk}}{r_k} \right) , \end{aligned}$$

(30)

where $\bar{r_l} = \sum _{k=1}^{K} \pi _{lk}r_k$ is the average channel rate for link l.

Furthermore, we know that the distribution of system waiting time for an M/G/1 system is (section 5.7 of [38]),

$$\begin{aligned} W(t;\tau _l) = (1-\gamma (\tau _l)) \sum _{n=0}^{\infty } \gamma ^n(\tau _l) \Psi ^{(n+1)}(t;\tau _l), \end{aligned}$$

(31)

where $\gamma (\tau _l)$ is server utilization and $\Psi ^{(n+1)}$ denotes the (n + 1)-fold convolution of the CDF of the residual service time, defined as

$$\begin{aligned} \Psi ^{(n+1)} (t;\tau _l) = \int _{x=0}^{\infty } \Psi ^{(n)} (x;\tau _l) \Psi (t-x;\tau _l) dx. \end{aligned}$$

(32)

Recalling that we require the delay violation probability to be bounded as,

$$\begin{aligned} {\mathsf {Pr}}(D > D_{l,max}) = 1-W(D_{l,max};\tau _l) \le \varepsilon _l, \end{aligned}$$

(33)

and using (31), it is sufficient to find the TXOP allocated to each link, $\tau _l$, such that,

$$\begin{aligned} \sum _{n=0}^{\infty } \gamma _l^n(\tau _l) \Psi _l^{(n+1)} (D_{l,max};\tau _l) \ge \frac{1-\varepsilon _l}{1-\gamma _l(\tau _l)}, \end{aligned}$$

(34)

where $\gamma _l(\tau _l)$ is the utilization of link l given by,

$$\begin{aligned} \gamma _l(\tau _l) = \frac{\lambda _l M \cdot BI}{\tau _l \sum _k \pi _{lk}r_k}. \end{aligned}$$

(35)