Multiple QoS provisioning with pre-emptive priority schedulers in multi-resource OFDMA networks

Abstract

In this paper, we present an analytical framework for the performance evaluation of a pre-emptive priority scheduler in multi-resource networks, like those using Orthogonal Frequency Division Multiple Access (OFDMA). We focus on Quality of Service (QoS)-guaranteed traffic for which QoS is guaranteed to individual users by restricting the number of admitted users. For this, the QoS-constrained capacity, in terms of the number of supported users, needs to be ascertained a priori. The QoS-constrained capacity is a function of users’ QoS requirements, channel conditions, and radio resource allocation algorithms, which in this work is the pre-emptive priority scheduler. It is, thus, a variable quantity and mostly obtained using time-consuming offline computer simulations. Mathematical models, on the other hand, are timely and accurate, allowing the capacity to be derived in real-time as a function of the current network configuration. Existing works on mathematical modelling of pre-emptive priority schedulers have mostly focussed on single servers or multiple servers where a single server is assigned to each user. In contrast, OFDMA networks have multiple radio resources, i.e., multiple servers and each user may need more than one radio resource for a single packet transmission, i.e. it is a multi-resource system, which has been accounted for in this paper. We classify the users based on their resource requirements and model the pre-emptive priority scheduler as a multi-class, multi-server, multi-resource, non-work conserving queueing system. We derive its QoS metrics like average delay, packet drop probability, throughput, etc., from its continuous-time Markov Chain. We then use the derived QoS metrics to obtain the QoS-constrained capacity and design a threshold based predictive call admission control unit. We have validated the results using extensive discrete event simulations.

Derivation of the rate of pre-emption

Pre-emptions occur when a class-$\textit{1}$ packet on arrival finds that fewer than $R_{req}^1$ servers are available. One or more class-$\textit{2}$ packets may have to be pre-empted to accommodate one class-$\textit{1}$ packet. So, $N_{2}^{P_d}$, i.e., the rate of pre-emption may be derived as:

$$\begin{aligned}&N_{2}^{P_d} \\ {}&=\mathrm {\frac{Total \ number \ of \ packets \ pre-empted}{Total \ arrival \ time}} \\&=\mathrm {\frac{ 1 \cdot no. \ of \ times \ 1 \ pkt. \ is \ pre-empted+ 2 \cdot no. \ of \ times \ 2 \ pkts \ are \ pre-empted+\cdots }{Total \ arrival \ time}} \\&=\mathrm {\frac{ 1 \cdot \frac{no. \ of \ times \ 1 \ pkt \ is \ pre-empted}{no. \ of \ class-1\ pkts}+ 2 \cdot \frac{no. \ of \ times \ 2 \ pkts \ are \ pre-empted}{no. \ of \ class-1 \ pkts}+\cdots }{\frac{Total \ arrival \ time}{no. \ of \ class-1 pkts}}} \\&=\mathrm {\frac{ 1 \cdot Prob. \ of \ pre-emption \ of \ 1 \ pkt.+ 2 \cdot Prob. \ of \ pre-emption \ of \ 2 \ pkts.+\cdots }{\frac{1}{\lambda _{p_1}}}} \\&=\lambda _{p_1}\cdot \mathrm {Average \ number \ of \ packets \ pre-empted}=\lambda _{p_1}\cdot N_{pre}^\mathbf{ ^{avg}} \end{aligned}$$

(21)

The average number of packets pre-empted per class-$\textit{1}$ arrival is $N_{pre}^\mathbf{ ^{avg}}=\sum \limits _{d=0}^{\infty }d*P_p^{d}$, where $P_p^{d}$ gives the probability that d number of packets are pre-empted. Using the CTMC in Fig. 2 and (15), the numbers of packets pre-empted in state ‘$\mathbf {s}$’$=(s_{n_{1}},s_{n_{2}},s_{b_{1}},s_{b_{2}})$ is $\left\lceil {\frac{R_{req}^1-N_s^{av}}{R_{req}^2}}\right\rceil =\left\lceil {\frac{R_{req}^1 -(\mathrm {N}_{\mathrm {PRB}}-\mathbf {s_{n_{}}}\cdot \mathbf {R_{req}})}{R_{req}^2}}\right\rceil$. So, $N_{pre}^\mathbf{ ^{avg}}$ may be expressed as:

$$\begin{aligned}&N_{pre}^\mathbf{ ^{avg}}= \sum \limits _{s_{n_{1}}}\sum \limits _{s_{n_{2}}=N_{pre}^2}^{\phi _{2,\phi _1}} \sum _{s_{b_{2}} = 0}^{L_2}\left\lceil {\frac{R_{req}^1-N_s^{av}}{R_{req}^2}}\right\rceil \pi _{(s_{n_{1}}, s_{n_{2}},0,s_{b_{2}})} \\&\quad {\forall s\in \mathcal {S}_{\mathcal {}}\ s.t.\ \frac{\mathrm {N}_{\mathrm {PRB}}-s_{n_{2}}R_{req}^2-R_{req}^1}{R_{req}^1}<s_{n_{1}} <\frac{N_{\mathrm {eff}_{1}}}{R_{req}^1}} \end{aligned}$$

(22)