Performance analysis for a stabilized multi-channel slotted ALOHA algorithm

We study slotted ALOHA with multiple random access channels, the so called multi-channel ALOHA (MC-ALOHA). It is well known that single-channel ALOHA (SC-ALOHA) is unstable. Not surprisingly, MC-ALOHA is also unstable. A stabilization algorithm for MC-ALOHA has been proposed in [10], in which the pseudo-Bayesian algorithm in SC-ALOHA was extended to achieve stabilized MC-ALOHA. The idea is to estimate the number of attempting users so that user transmission probability can be adjusted accordingly. In this paper, we give a theoretical analysis on the algorithm performance for cases with limited and unlimited number of users by assuming perfect estimate. The theoretical results are validated by simulation, which shows the stabilization algorithm performs close to a system with perfect estimate. The simulation results also show that the performance of the stabilized algorithm is much better than the non-stabilized algorithm. With the stabilized algorithm, the system is always stable when the new packet arrival rate is less than system capacity. Even when the arrival rate is higher than capacity, system throughput can still be guaranteed. © 2003 IEEE.published_or_final_versio

Stabilized multi-channel ALOHA for wireless OFDM networks

Multiple access based on orthogonal frequency division multiplexing (OFDM), or OFDMA, enables multiple users to simultaneously access the media by using different subcarriers. This leads to the convenient realization of multi-channel ALOHA, in which each user transmits with a group of subcarriers. In this paper, we first introduce the multi-channel slotted ALOHA algorithm to OFDM, which is called OFDMA-based multi-channel ALOHA (OMC-ALOHA). Since ALOHA is an unstable algorithm, we show OMC-ALOHA is also unstable. To solve this stability problem, we extend the pseudo-Bayesian algorithm to achieve stabilized OMC-ALOHA.published_or_final_versio

Stability Region of a Slotted Aloha Network with K-Exponential Backoff

Stability region of random access wireless networks is known for only simple network scenarios. The main problem in this respect is due to interaction among queues. When transmission probabilities during successive transmissions change, e.g., when exponential backoff mechanism is exploited, the interactions in the network are stimulated. In this paper, we derive the stability region of a buffered slotted Aloha network with K-exponential backoff mechanism, approximately, when a finite number of nodes exist. To this end, we propose a new approach in modeling the interaction among wireless nodes. In this approach, we model the network with inter-related quasi-birth-death (QBD) processes such that at each QBD corresponding to each node, a finite number of phases consider the status of the other nodes. Then, by exploiting the available theorems on stability of QBDs, we find the stability region. We show that exponential backoff mechanism is able to increase the area of the stability region of a simple slotted Aloha network with two nodes, more than 40\%. We also show that a slotted Aloha network with exponential backoff may perform very near to ideal scheduling. The accuracy of our modeling approach is verified by simulation in different conditions.Comment: 30 pages, 6 figure

On the Stability of Contention Resolution Diversity Slotted ALOHA

In this paper a Time Division Multiple Access (TDMA) based Random Access (RA) channel with Successive Interference Cancellation (SIC) is considered for a finite user population and reliable retransmission mechanism on the basis of Contention Resolution Diversity Slotted ALOHA (CRDSA). A general mathematical model based on Markov Chains is derived which makes it possible to predict the stability regions of SIC-RA channels, the expected delays in equilibrium and the selection of parameters for a stable channel configuration. Furthermore the model enables the estimation of the average time before reaching instability. The presented model is verified against simulations and numerical results are provided for comparison of the stability of CRDSA versus the stability of traditional Slotted ALOHA (SA). The presented results show that CRDSA has not only a high gain over SA in terms of throughput but also in its stability.Comment: 10 pages, 12 figures This paper is submitted to the IEEE Transactions on Communications for possible publication. The IEEE copyright notice applie

Age of Information in Random Access Channels

In applications of remote sensing, estimation, and control, timely communication is not always ensured by high-rate communication. This work proposes distributed age-efficient transmission policies for random access channels with $M$ transmitters. In the first part of this work, we analyze the age performance of stationary randomized policies by relating the problem of finding age to the absorption time of a related Markov chain. In the second part of this work, we propose the notion of \emph{age-gain} of a packet to quantify how much the packet will reduce the instantaneous age of information at the receiver side upon successful delivery. We then utilize this notion to propose a transmission policy in which transmitters act in a distributed manner based on the age-gain of their available packets. In particular, each transmitter sends its latest packet only if its corresponding age-gain is beyond a certain threshold which could be computed adaptively using the collision feedback or found as a fixed value analytically in advance. Both methods improve age of information significantly compared to the state of the art. In the limit of large $M$, we prove that when the arrival rate is small (below $\frac{1}{eM}$), slotted ALOHA-type algorithms are asymptotically optimal. As the arrival rate increases beyond $\frac{1}{eM}$, while age increases under slotted ALOHA, it decreases significantly under the proposed age-based policies. For arrival rates $\theta$, $\theta=\frac{1}{o(M)}$, the proposed algorithms provide a multiplicative factor of at least two compared to the minimum age under slotted ALOHA (minimum over all arrival rates). We conclude that, as opposed to the common practice, it is beneficial to increase the sampling rate (and hence the arrival rate) and transmit packets selectively based on their age-gain

Analysis of Slotted ALOHA with an Age Threshold

We present a comprehensive steady-state analysis of threshold-ALOHA, a distributed age-aware modification of slotted ALOHA proposed in recent literature. In threshold-ALOHA, each terminal suspends its transmissions until the Age of Information (AoI) of the status update flow it is sending reaches a certain threshold $\Gamma$. Once the age exceeds $\Gamma$, the terminal attempts transmission with constant probability $\tau$ in each slot, as in standard slotted ALOHA. We analyze the time-average expected AoI attained by this policy, and explore its scaling with network size, $n$. We derive the probability distribution of the number of active users at steady state, and show that as network size increases the policy converges to one that runs slotted ALOHA with fewer sources: on average about one fifth of the users is active at any time. We obtain an expression for steady-state expected AoI and use this to optimize the parameters $\Gamma$ and $\tau$, resolving the conjectures in \cite{doga} by confirming that the optimal age threshold and transmission probability are $2.2n$ and $4.69/n$, respectively. We find that the optimal AoI scales with the network size as $1.4169n$, which is almost half the minimum AoI achievable with slotted ALOHA, while the loss from the maximum throughput of $e^{-1}$ remains below $1\%$. We compare the performance of this rudimentary algorithm to that of the SAT policy that dynamically adapts its transmission probabilities