Related Work on Queueing Analysis for Wireless Transmission Systems

In general, in a wireless transmission system, arriving packets are buffered into radio link level queue before transmission to the target mobile (in downlink) or to the base station (in uplink). This buffering process causes delay in wireless transmission. Again, the transmission rate of a wireless channel varies due to variations in channel quality and channel errors. Therefore, a queueing analysis which can capture the channel and the radio link level buffer dynamics becomes a useful mathematical tool to investigate the QoS performances of a wireless transmission system. By using a queueing model, the performance results can be obtained more efficiently when compared with simulations. In addition, a queueing analytical model can be used not only to analyze the system's behavior under different parameter settings, but also to optimize the system performances in which several standard techniques in optimization (e.g., Markov decision process) can be applied.

Different queueing models for wireless transmission systems were proposed in the literature. Queueing analyses for a polling system and a system with cyclic service queues with Bernoulli scheduler were presented. These works considered only single rate transmission at the physical layer in which the modulation and coding scheme is fixed. On the other hand, multirate transmission based on adaptive modulation and coding (AMC) has been proposed in most of the current wireless standards to archive higher system capacity. Queueing analysis for radio link level scheduling with adaptive modulation in time division multiple access (TDMA) system was proposed. Also, a queueing model was used for optimizing the radio link level system parameters.

Multimedia services will be common in next generation wireless systems. A queueing model developed specifically for video source (e.g., MPEG traffic) was presented. In addition, the authors demonstrated how the video source coding parameters can be optimally adjusted to achieve the best performance. Again, in a multiservice traffic scenario, prioritization of real-time traffic over best-effort traffic is required. An analytical model for priority queueing was presented.

Combatting transmission errors due to interference and noise is one of the challenging issues in wireless transmission systems. Automatic Repeat reQuest (ARQ) is one of these methods to recover erroneous transmissions. When a transmission fails (i.e., the receiver cannot decode the transmitted information correctly), the receiver requests the transmitter to retransmit. Different variants of ARQ can be used (e.g., probabilistic retransmission, finite and infinite retransmission). Queueing models with ARQ mechanism were proposed. For example, queueing models for go-back-N and selective repeat ARQ were presented. Since with AMC multiple packets can be transmitted in one time slot, if an error occurs, N packets up to the last transmission will be retransmitted for go-back-N ARQ and only the erroneous packets will be retransmitted in case of selective repeat ARQ. Due to the time and space-dependent wireless channel errors and the burstiness of the errors, some connections could experience inferior performance compared with the others. Therefore, a compensation mechanism was introduced to maintain fairness (by allowing more transmissions in the current time frame to compensate errors in the previous time frame) and guarantee the target QoS performance. Also, a queueing model for this compensation mechanism was proposed.

In a multi-user wireless system, packet scheduling is required to allocate the available transmission resources to the ongoing users in a fair and efficient manner. Various packet scheduling policies were proposed in the literature. The most common policy is fair scheduling in which the ongoing users receive services based on their preassigned weights. A queueing model for this scheduling policy in a wireless transmission environment was presented. On the other hand, opportunistic scheduling was developed specifically for wireless transmission systems. This scheduling policy takes advantage of multi-user diversity to improve the throughput of the entire system. In particular, the user who has the best channel quality in the current time slot will be selected to transmit. A queueing model of this scheduling policy was proposed. In addition, queueing analyses for different resource-sharing schemes (i.e., max-min fairness, proportional fairness, and balanced fairness) were presented. Also, the stability condition for each of the schemes was studied.

While most of the queueing models in the literature considered only the variation of wireless channel on system performance, a few works considered the impacts of resource allocation and admission control on queueing performance. For example, impacts of resource allocation and admission were considered in the queueing model for a TDMA-based cellular wireless system  using adaptive modulation and coding, and a code division multiple access (CDMA)-based system  with rate adaptation. These investigations showed that resource reservation for handoff connections (i.e., through guard channel) as well as the transmission rate adaptation can impact the queueing performance of the mobile users significantly.

Queueing analysis can be also used for the development of admission control mechanisms. This approach was presented in the literature. In particular, given the traffic parameters and the estimated wireless channel quality, for a given medium access control mechanism, information on queueing delay and packet loss can be obtained and used by the admission controller to decide whether a new connection can be accepted or not. The decision on acceptance or rejection of a new connection is based on whether the QoS performances of both the ongoing connections and the new connection can be maintained at the target level or not. A queueing model was presented which could be used for admission control in Bluetooth-based wireless personal area networks (PANs). A queueing model for IEEE 802.11-based wireless local area networks (WLANs) was proposed. In these works, the MAC protocol was assumed to be carrier sense multiple access/collision avoidance (CSMA/CA).

In addition to the traditional wireless systems which rely on the Single-Input Single-Output (SISO) transmission, Multiple-Input Multiple-Output (MIMO) system has been developed to provide better performance in terms of error or transmission rate. A queueing model for MIMO system was proposed in which the advantages of spatial diversity in terms of smaller queueing delay and packet loss were demonstrated.

Multihop communication will be a significant component in the next generation wireless systems. In a multihop network, the transmission range of a transmitter (e.g., in the base station) can be extended by relaying the traffic through multiple intermediate nodes. This multihop transmission is a common feature in wireless ad hoc, mesh, and sensor networks. Queueing models for this multihop wireless communication were proposed in the literature. For example, end-to-end performances of a multihop wireless network in terms of latency, reliability, and throughput were studied through a queueing model considering adaptive modulation and coding at the physical layer. A tandem queueing model for multihop transmission was presented in. For sensor networks, energy conservation is one of the challenging issues. Since the amount of energy available at a sensor node is limited (e.g., due to battery size or energy-harvesting technology such as a solar cell), an energy saving mechanism is required and it can impact the wireless transmission performance significantly. A queueing model for sensor networks with energy conservation feature through sleep and wake-up mechanism was presented. A vacation queueing model was used to investigate the inter-relationship between the transmission performance and the energy consumption.