We consider a system model with two sources, a reliable source and an unreliable source, who are responsible for disseminating updates regarding a process to an age-based gossip network ofnnodes. Nodes wish to have fresh information, however, they have preference for packets that originate at the reliable source and are willing to sacrifice their version age of information by up toGversions to switch from an unreliable packet to a reliable packet. We study how this protocol impacts the prevalence of unreliable packets at nodes in the network and their version age. Using a stochastic hybrid system (SHS) framework, we formulate analytical equations to characterize two quantities: expected fraction of nodes with unreliable packets and expected version age of information at network nodes. We show that asGincreases, fewer nodes have unreliable packets, however, their version age increases as well, thereby inducing a freshness-reliability trade-off in the network. We further investigate the dependence of network reliability and freshness on various network parameters, such as, inter-node update rates and the network size. We support our analytical findings by extensive numerical and simulation results.

Mixture-of-Agents (MoA) has recently been proposed as a method to enhance performance of large language models (LLMs), enabling multiple individual LLMs to work together for collaborative inference. This collaborative approach results in improved responses to user prompts compared to relying on a single LLM. In this paper, we consider such an MoA architecture in a distributed setting, where LLMs operate on individual edge devices, each uniquely associated with a user and equipped with its own distributed computing power. These devices exchange information using decentralized gossip algorithms, allowing different device nodes to talk without the supervision of a centralized server. In the considered setup, different users have their own LLM models to address user prompts. Additionally, the devices gossip either their own user-specific prompts or augmented prompts to generate more refined answers to certain queries. User prompts are temporarily stored in the device queues when their corresponding LLMs are busy. Given the memory limitations of edge devices, it is crucial to ensure that the average queue sizes in the system remain bounded. In this paper, we address this by theoretically calculating the queuing stability conditions for the device queues under reasonable assumptions, which we validate experimentally as well. Further, we demonstrate through experiments, leveraging open-source LLMs for the implementation of distributed MoA, that certain MoA configurations produce higher-quality responses compared to others, as evaluated on AlpacaEval 2.0 benchmark. The implementation is available at: https://github.com/purbeshmitra/distributed_moa.

Gossiping is a communication mechanism, used for fast information dissemination in a network, where each node of the network randomly shares its information with the neighboring nodes. To characterize the notion of fastness in the context of gossip networks, age of information (AoI) is used as a timeliness metric. In this article, we summarize the recent works related to timely gossiping in a network. We start with the introduction of randomized gossip algorithms as an epidemic algorithm for database maintenance, and how the gossiping literature was later developed in the context of rumor spreading, message passing and distributed mean estimation. Then, we motivate the need for timely gossiping in applications such as source tracking and decentralized learning. We evaluate timeliness scaling of gossiping in various network topologies, such as, fully connected, ring, grid, generalized ring, hierarchical, and sparse asymmetric networks. We discuss age-aware gossiping and the higher order moments of the age process. We also consider different variations of gossiping in networks, such as, file slicing and network coding, reliable and unreliable sources, information mutation, different adversarial actions in gossiping, and energy harvesting sensors. Finally, we conclude this article with a few open problems and future directions in timely gossiping.

We study timeliness in cache-aided networks where the inter-update times on the links are not necessarily exponentially distributed. We focus on the set of non-arithmetic distributions for inter-update times, which includes continuous probability distributions as a subset. We first characterize instantaneous age of information at each node for arbitrary networks. We then explicate the recursive equations for instantaneous age of information in multi-hop networks and use them to derive closed form expressions for expected age of information at an end-user in tree networks. We show that expected age in multi-hop networks exhibits an additive structure. Further, we show that the expected age at each user is directly proportional to the variance of the inter-update times at all links between a user and the source. We next prove analogous results for the version age of information in multi-hop networks where updates at the source are marked with incrementing version numbers. We show that expected version age at end-users is inversely proportional to the mean update interval at the source, and exhibits an additive structure. Finally, we study expected age of information in networks with the property that the update processes on the links become sparse for large network sizes, and remark that expected age scales as$O(\log {n})$in symmetric fully connected networks. We expect the analysis in this work to help alleviate the over-dependence on exponential inter-update time (i.e., Poisson) updates for future work in age of information.

The rapid dissemination of real-time updates in interconnected networks often encounters the challenge of misinformation spreading alongside accurate information. This paper examines the interplay between timeliness and accuracy of updates in fully-connected gossip networks, where probabilistic mutations during transmission can convert truth into misinformation. We consider a network ofnuser nodes that receives updates from a source and employs an age-based gossip protocol for faster dissemination of version updates to all nodes. When a node forwards its packet to another node, the packet information gets mutated with probabilitypduring transmission, creating misinformation. The receiver node does not know whether an incoming packet contains correct information or misinformation. The receiver runs a gossip protocol that looks only at the version age of the incoming packet and accepts it if it is fresher than the packet in its possession. For the case when the incoming packet has the same version age as the receiver’s own packet, we consider two system models: In the first model, we assume that truth prevails over misinformation, and therefore, when a receiver encounters both accurate information and misinformation corresponding to the same version, the accurate information gets chosen for storage at the node. In the second model, we assume the opposite scenario, where misinformation prevails over truth. For both models, we study the expected fraction of nodes with correct information in the network and the version age at the nodes using the stochastic hybrid systems (SHS) method. We observe that when truth prevails over misinformation, very high or very low gossiping rates help curb misinformation, and misinformation spread is higher with moderate gossiping rates. However, when misinformation prevails, misinformation rises with increased inter-node gossiping. We support our theoretical findings with simulation results which shed further light on the behavior of the above studied quantities.

We consider a communication system consisting of a server that tracks and publishes updates about a time-varying data source or event, and a gossip network of users interested in closely tracking the event. The timeliness of the information is measured through the version age of information. The users wish to have their expected version ages remain below a threshold, and have the option to either rely on gossip from their neighbors or subscribe to the server directly to follow updates about the event if the former option does not meet the timeliness requirements. The server wishes to maximize its profit by increasing the number of subscribers and reducing costs associated with the frequent sampling of the event. We model the problem setup as a Stackelberg game between the server and the users, where the server commits to a frequency of sampling the event, and the users make decisions on whether to subscribe or not. As an initial work, we focus on directed networks with unidirectional flow of information and obtain the optimal equilibrium strategies for all the players. We provide simulation results to confirm the theoretical findings and provide additional insights.

We consider a system model with two sources, a reliable source and an unreliable source, who are responsible for disseminating updates regarding a process to an age-based gossip network of$n$nodes. Nodes wish to have fresh information, however, they have preference for packets that originated at the reliable source and are willing to sacrifice their version age of information by up to$G$versions to switch from an unreliable packet to a reliable packet. We study how this protocol impacts the prevalence of unreliable packets at nodes in the network and their version age. Using a stochastic hybrid system (SHS) framework, we formulate analytical equations to characterize two quantities: expected fraction of nodes with unreliable packets and expected version age of information at network nodes. We show that as$G$increases, fewer nodes have unreliable packet, however, their version age increases as well, thereby inducing a freshness-reliability trade-off in the network. We present numerical results to support our findings.

We consider gossip networks consisting of a source that maintains the current version of a file, n nodes that use asynchronous gossip mechanisms to disseminate fresh information in the network, and an oblivious adversary who infects the packets at a target node through data timestamp manipulation, with the intent to replace circulation of fresh packets with outdated packets in the network. We demonstrate how network topology capacitates an adversary to influence age scaling in a network. We show that in a fully connected network, a single infected node increases the expected age from O(log n) to O(n). Further, we show that the optimal behavior for an adversary is to reset the timestamps of all outgoing packets to the current time and of all incoming packets to an outdated time for the infected node; thereby preventing any fresh information to go into the infected node, and facilitating acceptance of stale information out of the infected node into other network nodes. Additionally, if the adversary allows the infected node to accept a small fraction of incoming packets from the network, then a large network can manage to curb the spread of stale files coming from the infected node and pull the network age back to O(log n). Lastly for fully connected network, we show that if an infected node contacts only a single node instead of all nodes of the network, the system age can still be degraded to O(n). These show that fully connected nature of a network can be both a benefit and a detriment for information freshness; full connectivity, while enabling fast dissemination of information, also enables fast dissipation of adversarial inputs. We then analyze the unidirectional ring network, the other end of the network connectivity spectrum, where we show that the adversarial effect on age scaling of a node is limited by its distance from the adversary, and the age scaling for a large fraction of the network continues to be O(√n), unchanged from the case with no adversary. We finally support our findings with simulations.

We consider a system consisting of a server, which receives updates for$N$files according to independent Poisson processes. The goal of the server is to deliver the latest version of the files to a user through a parallel network of$K$caches. We consider an update received by the user successful, if the user receives the same file version that is currently prevailing at the server. We derive an analytical expression for information freshness at the user. We observe that freshness for a file increases with increase in consolidation of rates across caches. To solve the multi-cache problem, we first solve the auxiliary problem of a single-cache system. We then rework this auxiliary solution to our parallel-cache network by consolidating rates to single routes as much as possible. This yields an approximate (sub-optimal) solution for the original problem. We provide an upper bound on the gap between the sub-optimal solution and the optimal solution. We present counterpart expressions and policies for version age of information by employing a stochastic hybrid system approach. Numerical results for both timeliness metrics show that the proposed sub-optimal policy closely follows the optimal policy.

We consider a network of$n$user nodes that receives updates from a source and employs an age-based gossip protocol for faster dissemination of version updates to all nodes. When a node forwards its packet to another node, the packet information gets mutated with probability$p$during transmission, creating misinformation. The receiver node does not know whether an incoming packet information is different from the packet information originally at the sender node. We assume that truth prevails over misinformation, and therefore, when a receiver encounters both accurate information and misinformation corresponding to the same version, the accurate information gets chosen for storage at the node. We study the expected fraction of nodes with correct information in the network and version age at the nodes in this setting using stochastic hybrid systems (SHS) modelling and study their properties. We observe that very high or very low gossiping rates help curb misinformation, and misinformation spread is higher with moderate gossiping rates. We support our theoretical findings with simulation results which shed further light on the behavior of above quantities.

We study age of information in multi-hop multi-cast cache-enabled networks where the inter-update times on the links are not necessarily exponentially distributed. We focus on the set of non-arithmetic distributions for inter-update times, which includes continuous probability distributions as a subset. We first characterize instantaneous age of information at each node for arbitrary networks. We then explicate the recursive equations for instantaneous age of information in multi-hop networks and derive closed form expressions for expected age of information at an end-user. We show that expected age in multi-hop networks exhibits an additive structure. Further, we show that the expected age at each user is directly proportional to the variance of inter-update times at all links between a user and the source. We expect the analysis in this work to help alleviate the over-dependence on Poisson processes for future work in age of information.

We consider a network consisting of n nodes that aim to track a continually updating process or event. To disseminate updates about the event to the network, two sources are available, such that information obtained from one source is considered more reliable than the other source. The nodes wish to have access to information about the event that is not only latest but also more reliable, and prefer a reliable packet over an unreliable packet even when the former is a bit outdated with respect to the latter. We study how such preference affects the fraction of users with reliable information in the network and their version age of information. We derive the analytical equations to characterize the two quantities, long-term expected fraction of nodes with reliable packets and their long-term expected version age using stochastic hybrid systems (SHS) modelling and study their properties. We also compare these results with the case where nodes give more preference to freshness of information than its reliability. Finally we show simulation results to verify the theoretical results and shed further light on behavior of above quantities with respect to dependent variables.

We consider a slotted communication system consisting of a source, a cache, a user and a timestomping adversary. The time horizon consists of total$T$time slots, such that the source transmits update packets to the user directly over$T_1$time slots and to the cache over$T_{2}$time slots. We consider$T_{1}\ll T_{2}, T_{1}+T_{2} < T$, such that the source transmits to the user once between two consecutive cache updates. Update packets are marked with timestamps corresponding to their generation times at the source. All nodes have a buffer size of one and store the packet with the latest timestamp to minimize their age of information. In this setting, we consider the presence of an oblivious adversary that fully controls the communication link between the cache and the user. The adversary manipulates the timestamps of outgoing packets from the cache to the user, with the goal of bringing staleness at the user node. At each time slot, the adversary can choose to either forward the cached packet to the user, after changing its timestamp to current time$t$, thereby rebranding an old packet as a fresh packet and misleading the user into accepting it, or stay idle. The user compares the timestamps of every received packet with the latest packet in its possession to keep the fresher one and discard the staler packet. If the user receives update packets from both cache and source in a time slot, then the packet from source prevails. The goal of the source is to design an algorithm to minimize the average age at the user, and the goal of the adversary is to increase the average age at the user. We formulate this problem in an online learning setting and provide a fundamental lower bound on the competitive ratio for this problem. We further propose a deterministic algorithm with a provable guarantee on its competitive ratio.

We consider a system consisting of a large network of n users and a library of files, wherein inter-user communication is established based upon gossip mechanisms. Each file is initially present at exactly one node, which is designated as the file source. The source gets updated with newer versions of the file according to an arbitrary distribution in real time, and the other users in the network wish to acquire the latest possible version of the file. We present a class of gossip protocols that achieve O(1) age at a typical node in a single-file system and O(n) age at a typical node for a given file in an n-file system. We show that file slicing and network coding based protocols fall under the presented class of protocols. Numerical evaluation results are presented to confirm the aforementioned bounds.

We consider a fully connected network consisting of a source that maintains the current version of a file, n nodes that use asynchronous gossip mechanisms to disseminate fresh information in the network, and an adversary who infects the packets at a target node through data timestamp manipulation, with the intent to replace circulation of fresh packets with outdated packets in the network. We show that a single infected node increases the expected age of a fully connected network from O(log n) to O(n). Further, we show that the optimal behavior for an adversary is to reset the timestamps of all outgoing packets to the current time and of all incoming packets to an outdated time. Additionally, if the adversary allows the infected node to accept a small fraction of incoming packets from the network, then a large network can manage to curb the spread of stale files coming from the infected node and pull the network age back to O(log n). Lastly, we show that if an infected node contacts only a single node instead of all nodes of the network, the system age can still be degraded to O(n). These show that fully connected nature of a network can be both a benefit and a detriment for information freshness; full connectivity, while enabling fast dissemination of information, also enables fast dissipation of adversarial inputs.

We consider a system consisting of a server, which receives updates for$N$files according to independent Poisson processes. The goal of the server is to deliver the latest version of the files to the user through a parallel network of$K$caches. We consider an update received by the user successful, if the user receives the same file version that is currently prevailing at the server. We derive an analytical expression for information freshness at the user. We observe that freshness for a file increases with increase in consolidation of rates across caches. To solve the multi-cache problem, we first solve the auxiliary problem of a single-cache system. We then rework this auxiliary solution to our parallel-cache network by consolidating rates to single routes as much as possible. This yields an approximate (sub-optimal) solution for the original problem. We provide an upper bound on the gap between the sub-optimal solution and the optimal solution. Numerical results show that the sub-optimal policy closely approximates the optimal policy.