Mobile Information Systems

Volume 2015 (2015), Article ID 157659, 9 pages

http://dx.doi.org/10.1155/2015/157659

## End-to-End Delay Analysis in Cognitive Radio Ad Hoc Networks with Different Traffic Models

^{1}School of Electronics and Communication Engineering, Tianjin Normal University, Tianjin 300387, China^{2}Beijing Key Laboratory of Network System Architecture and Convergence, Beijing University of Posts and Telecommunications, Beijing 100876, China^{3}Information Network Center, Beijing University of Posts and Telecommunications, Beijing 100876, China

Received 8 June 2015; Accepted 12 July 2015

Academic Editor: Qilian Liang

Copyright © 2015 Jing Gao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Delay and throughput are important metrics for network performance. We analyze the end-to-end delay of cognitive radio ad hoc networks for two traffic models: backlogged and geometric, respectively. By modelling the primary users as a Poisson point process and the secondary network deploying multihop transmissions, we derive the closed-form expression for the end-to-end delay in secondary networks. Furthermore, we optimize the end-to-end delay in terms of the hop number and the secondary transmission probability, respectively. The range of the optimal hop number and the equation satisfied by the optimal transmission probability are obtained for backlogged source models. The equation met by the optimal hop number is presented for geometric source models.

#### 1. Introduction

With the rapid development of real-time transmissions in wireless communication networks, delay analysis has gained more and more attention in the literature. Compared with single-hop transmission, the analysis of multihop delay is more challenging. Since many factors can impact the end-to-end delay in multihop networks, such as routing algorithm, network topology, traffic model, and data scheduling, and since it is unrealistic to analyze the end-to-end delay by taking all factors into consideration, we simplify the network topology as a “line network” by neglecting the routing algorithm to complete the analysis of end-to-end delay.

A “line network” consists of a source, many relays, and a destination with all relays being distributed along line from a source to its destination. So far, much research has been conducted on the performance of “line network.” In [1, 2], end-to-end propagation speed is determined without the delay constraints with a channel model combined path-loss, fading with noise. Accordingly, the tradeoff between single-hop transmission and multihop transmission subject to an end-to-end delay constraint is studied in [3]. In [4], end-to-end packet delivery probability is derived based on the distances between neighboring nodes in a Poisson point process (PPP). In [5], “line network” is decomposed into many independent queues, and the end-to-end delay is determined by considering the combination of TDMA and ALOHA access protocol. All these works do not take the traffic style of the source node into consideration. With the increasing requirement for various types of traffic [6, 7] (such as document, video, and audio), it becomes important to characterize the network performance considering different types of traffic. In [8], the correlations between traffic statistics and channel qualities are investigated accompanied with their impact on the performance of multihop networks. In [9], the end-to-end delay is studied in Poisson network considering two traffic models: backlogged and geometric.

However, prior studies only focused on homogeneous networks without considering heterogeneous network model. A practical network usually consists of interdependent, interactive, and hierarchical network components which leads to a heterogeneous network structure. Different from [9], the purpose of this paper is to conduct a systematic study of the end-to-end delay in cognitive radio (CR) ad hoc networks which is one of heterogeneous network models. In this paper, we evaluate the end-to-end delay of CR ad hoc networks in which the secondary nodes are assumed to be placed to form a line network. We derive the closed-form expression for the end-to-end delay for backlogged and geometric arrival model of source traffic, respectively. Primary and secondary networks are supposed to be two PPPs which are independent of each other. Similar to that, in [9], waiting delay is considered by importing the node buffer accompanied with propagation delay. And the waiting delay of each node is modeled as a M/M/1 model with infinite buffer.

The paper is organized as follows. Section 2 defines the system model and symbol notations. Section 3 analyzes the end-to-end delay of CR ad hoc network. Section 4 derives the end-to-end delay of secondary network for two traffic models. Section 5 presents the numerical results and some discussions. Finally, conclusions are drawn in Section 6.

#### 2. System Model

We consider a scenario where primary users and secondary users coexist in the same two-dimensional plane. Secondary users employ underlay spectrum sharing method to access the licensed channel, that is, transmit their packets while keeping the quality of service (QoS) of primary network. In the following, we will define the primary and secondary network models, respectively.

##### 2.1. Primary Network Model

Assume that the locations of primary transmitters follow a PPP with density . Each primary receiver associates with one designated primary transmitter with distant away. According to the displacement theorem [10], the locations of the primary receivers formulate another PPP with density . All transmitters are assumed to send their packets with the same power . Signals undergo path-loss and small scale Rayleigh fading so that the power caught by a receiver is , where is the small scale fading coefficient having exponential distribution with mean of 1 and is the path-loss factor.

##### 2.2. Secondary Network Model

###### 2.2.1. Topology

Secondary network is composed of many multihop paths, each of which comprises a source user, relay users, and a destination user. The distance from a source user to its destination is . Figure 1 is the topology of a two-hop network. Supposing that all source users are distributed as a PPP with density , then all relay users formulate a PPP with density . All relay users are equidistantly distributed on the line from source user to the destination user; one hop distance is . Index as the source, the relay, and destination users. The power of all transmitters is assumed to be the same and is represented by . Time is divided into slots and all users are synchronized to one clock. We assume no space reuse on one path; that is, users along one path are not allowed to send packets in the same time slot. Therefore, the locations of secondary transmitters in each slot follow a PPP with density . Each user has an infinite buffer in which data is queued by FIFO (first-in-first-out) mode.