Prophet Matching with General Arrivals

We provide prophet inequality algorithms for online weighted matching in general (nonbipartite) graphs, under two well-studied arrival models: edge arrival and vertex arrival. The weights of the edges are drawn from a priori known probability distribution. Under edge arrival, the weight of each edge is revealed on arrival, and the algorithm decides whether to include it in the matching or not. Under vertex arrival, the weights of all edges from the newly arriving vertex to all previously arrived vertices are revealed, and the algorithm decides which of these edges, if any, to include in the matching. To study these settings, we introduce a novel unified framework of batched-prophet inequalities that captures online settings where elements arrive in batches. Our algorithms rely on the construction of suitable online contention resolution scheme (OCRS). We first extend the framework of OCRS to batched-OCRS, we then establish a reduction from batched-prophet inequality to batched-OCRS, and finally we construct batched-OCRSs with selectable ratios of 0.337 and 0.5 for edge and vertex arrival models, respectively. Both results improve the state of the art for the corresponding settings. For vertex arrival, our result is tight. Interestingly, a pricing-based prophet inequality with comparable competitive ratios is unknown.

Coherent Contention Resolution Diversity Slotted ALOHA: An Improved Multiple Access Method for Satellite IoT System

For Beyond 5G/6G system, satellite communication systems become an effective component of the space and terrestrial integrated network. Among typical applications, massive Machine Type of Communication (mMTC) is a promising and challenging application. The demands of low power consumption and light signaling make random access methods as the potential solution. Up to now, contention resolution-based ALOHA methods, such as contention resolution diversity slotted ALOHA (CRDSA), improve the throughput significantly. However, its throughput will meet the inflection point soon with the normalized load increasing since collisionless packets are hardly existing. In fact, the diversity of transmitting packets is not utilized totally. In this paper, an improved random access method, named coherent CRDSA method (C-CRDSA), is proposed. It accumulates replicated packets coherently at receiver and further improve the throughput over CRDSA. Detailed derivations and simulations are given. Simulation results corroborate the effectiveness of the proposed method.

Design of optical packet switch in presence of dispersion compensation and amplifier noise

Optical communication gained popularity in past few years. Optical communication has many distinct advantages over copper cable based electronic communication. Optical switches are integral part of optical networks which are used for rerouting of packets and also plays important role in contention resolution of the packets. These switch uses fiber delay lines (FDLs) act as optical memory. In past analysis of the switch is done by considering loss, power and noise and finally bit error rate (BER); however dispersion was neglected which is an important parameter in high speed communication. In this paper, design analysis is done by considering dispersion compensation along with optical amplifier noise.