Recent advancements in Large Language Models (LLMs) have transformed many fields including scientific discovery, content generation, biomedical text mining, and educational technology. However, the substantial requirements for training data, computational resources, and energy consumption pose significant challenges for their practical deployment. A promising alternative is to leverage smaller, specialized language models and aggregate their outputs to improve overall response quality. In this work, we investigate a networked LLM system composed of multiple users, a central task processor, and clusters of topic-specialized LLMs. Each user submits categorical binary (true/false) queries, which are routed by the task processor to a selected cluster of $m$ LLMs. After gathering individual responses, the processor returns a final aggregated answer to the user. We characterize both the information accuracy and response timeliness in this setting, and formulate a joint optimization problem to balance these two competing objectives. Our extensive simulations demonstrate that the aggregated responses consistently achieve higher accuracy than those of individual LLMs. Notably, this improvement is more significant when the participating LLMs exhibit similar standalone performance.

We consider a single large language model (LLM) server that serves a heterogeneous stream of queries belonging to $N$ distinct task types. Queries arrive according to a Poisson process, and each type occurs with a known prior probability. For each task type, the server allocates a fixed number of internal thinking tokens, which determines the computational effort devoted to that query. The token allocation induces an accuracy-latency trade-off: the service time follows an approximately affine function of the allocated tokens, while the probability of a correct response exhibits diminishing returns. Under a first-in, first-out (FIFO) service discipline, the system operates as an $M/G/1$ queue, and the mean system time depends on the first and second moments of the resulting service-time distribution. We formulate a constrained optimization problem that maximizes a weighted average accuracy objective penalized by the mean system time, subject to architectural token-budget constraints and queue-stability conditions. The objective function is shown to be strictly concave over the stability region, which ensures existence and uniqueness of the optimal token allocation. The first-order optimality conditions yield a coupled projected fixed-point characterization of the optimum, together with an iterative solution and an explicit sufficient condition for contraction. Moreover, a projected gradient method with a computable global step-size bound is developed to guarantee convergence beyond the contractive regime. Finally, integer-valued token allocations are attained via rounding of the continuous solution, and the resulting performance loss is evaluated in simulation results.

With the widespread adoption of internet-of-things (IoT) devices capable of supporting numerous intelligent applications, the demand for computational power has surged dramatically. Multi-access edge computing (MEC) technology is a promising solution to assist the often power-constrained IoT devices by providing additional computing resources for time-sensitive tasks. In this paper, we consider the problem of optimal task offloading in MEC systems with due consideration of the timeliness and scalability issues under two scenarios of equitable and priority access to the edge server (ES). In the first scenario, we consider a MEC system consisting of$N$devices assisted by one ES, where the devices can split task execution between a local processor and the ES, withequitable accessto the ES. In the second scenario, we consider a MEC system consisting of one primary user,$N$secondary users and one ES. The primary user haspriority accessto the ES while the secondary users haveequitable accessto the ES amongst themselves. In both scenarios, due to the power consumption associated with utilizing the local resource and task offloading, the devices must optimize their actions. Additionally, since the ES is a shared resource, other users' offloading activity serves to increase latency incurred by each user. We thus model both scenarios using alarge usernon-cooperative game framework. However, the presence of a large number of users makes it nearly impossible to compute the equilibrium offloading policies for each user, which would require a significant communication overhead to exchange information with each other. Thus, to alleviate such scalability issues, we invoke the paradigm of mean-field games (MFGs) to design completely distributed low complexity algorithms for the computation of approximate Nash equilibrium policies for each user based on only their local information. Further, by leveraging the novel age of information (AoI) metric, we study the trade-offs between increasing information freshness and reducing power consumption for each user. Using numerical evaluations, we show that our approach can recover the offloading trends displayed under centralized solutions, and provide additional insights into the results obtained.

We consider the problem of assigning tasks efficiently to a set of workers that can exhaust themselves as a result of processing tasks. If a worker is exhausted, it will take a longer time to recover. To model efficiency of workers with exhaustion, we use a continuous-time Markov chain (CTMC). By taking samples from the internal states of the workers, the source assigns tasks to the workers when they are found to be in their efficient states. We consider two different settings where (i) the source can assign tasks to the workers only when they are in their most efficient state, and (ii) it can assign tasks to workers when they are also moderately efficient in spite of a potentially reduced success probability. In the former case, we find the optimal policy to be a threshold-based sampling policy where the thresholds depend on the workers’ recovery and exhaustion rates. In the latter case, we solve a non-convex sum-of-ratios problem using a branch-and-bound approach which performs well compared with the globally optimal solution.

We consider an information update system on a gossip network, where a source node encodes information intontotal keys such that any subset of at leastk+ 1 keys can fully reconstruct the original information. This encoding process follows the principles of ak-out-of-nthreshold system. The encoded updates are then disseminated across the network through peer-to-peer communication. We have two different types of nodes in a network: subscriber nodes, which receive a unique key from the source node for every status update instantaneously, and nonsubscriber nodes, which receive a unique key for an update only if the node is selected by the source, and this selection is renewed for each update. For the message structure between nodes, we consider two different schemes: a memory scheme (in which the nodes keep the source’s current and previous encrypted messages) and a memoryless scheme (in which the nodes are allowed to only keep the source’s current message). We measure thetimelinessof information updates by using a recent performance metric called, the version age of information. We present explicit formulas for the time average AoI in a scalable homogeneous network as functions of the number of subscriber nodes under a memoryless scheme. Additionally, we provide strict lower and upper bounds for the time average AoI under a memory scheme.

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.

Most existing stochastic models on age of information (AoI) focus on a single shared server serving status update packets from N > 1 sources where each packet update stream is Poisson, i.e., single-hop scenario. In the current work, we study a two-hop edge computing system for which status updates from the information sources are still Poisson but they are not immediately available at the shared edge server, but instead they need to first receive service from a transmission server dedicated to each source. For exponentially distributed and heterogeneous service times for both the dedicated servers and the edge server, and bufferless preemptive resource management, we develop an analytical model using absorbing Markov chains (AMC) for obtaining the distribution of AoI for any source in the system. Moreover, for a given tagged source, the traffic arriving at the shared server from the N - 1 un-tagged sources, namely the interference traffic, is not Poisson any more, but is instead a Markov modulated Poisson process (MMPP) whose state space grows exponentially with N. Therefore, we propose to employ a model reduction technique that approximates the behavior of the MMPP interference traffic with two states only, making it possible to approximately obtain the AoI statistics even for a very large number of sources. Numerical examples are presented to validate the proposed exact and approximate models.

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 information dissemination over a network of gossiping agents (nodes). In this model, a source keeps the most up-to-date information about a time-varying binary state of the world, and n receiver nodes want to follow the information at the source as accurately as possible. When the information at the source changes, the source first sends updates to a subset of m≤n nodes. After that, the nodes share their local information during the gossiping period to disseminate the information further. The nodes then estimate the information at the source using the majority rule at the end of the gossiping period. To analyze information dissemination, we introduce a new error metric to find the average percentage of nodes that can accurately obtain the most up-to-date information at the source. We characterize the equations necessary to obtain the steady-state distribution for the average error. Through numerical results, we first show that when the source’s transmission capacity m is limited, gossiping can be harmful as it causes incorrect information to disseminate. We then find the optimal gossip rates to minimize the average error for a fixed m.

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.

An information source generates independent and identically distributed status update messages from an observed random phenomenon which takes n distinct values based on a given probability mass function (PMF). These update packets are encoded at the transmitter node to be sent to a receiver node which wants to track the observed random variable with as little age as possible. The transmitter node implements a selective k encoding policy such that rather than encoding all possible n realizations, the transmitter node encodes the most probable k realizations. We consider three different policies regarding the remaining n-k less probable realizations: highest k selective encoding which disregards whenever a realization from the remaining n-k values occurs; randomized selective encoding which encodes and sends the remaining n-k realizations with a certain probability to further inform the receiver node at the expense of longer codewords for the selected k realizations; and highest k selective encoding with an empty symbol which sends a designated empty symbol when one of the remaining n-k realizations occurs. For all of these three encoding schemes, we find the average age and determine the age-optimal real codeword lengths, including the codeword length for the empty symbol in the case of the latter scheme, such that the average age at the receiver node is minimized. Through numerical evaluations for arbitrary PMFs, we show that these selective encoding policies result in a lower average age than encoding every realization, and find the corresponding age-optimal k values. Since we focus on real-valued codeword lengths in this paper, the resulting age value obtained in each case studied here serves as a lower bound to what can be attained by integer-valued codeword lengths in that case.

We consider an information update system where an information receiver requests updates from an information provider in order to minimize its age of information. The updates are generated at the information provider (transmitter) as a result of completing a set of tasks such as collecting data and performing computations on them. We refer to this as the update generation process. We model thequalityof an update as an increasing function of the processing time spent while generating the update at the transmitter. In particular, we usedistortionas a proxy forquality, and model distortion as a decreasing function of processing time. Processing longer at the transmitter results in a better quality (lower distortion) update, but it causes the update to age in the process. We determine the age-optimal policies for the update request times at the receiver and the update processing times at the transmitter subject to a minimum required quality (maximum allowed distortion) constraint on the updates. For the required quality constraint, we consider the cases of constant maximum allowed distortion constraints, as well as age-dependent maximum allowed distortion constraints.

We consider a cache updating system with a source, a cache and a user. There are n files. The source keeps the freshest version of the files which are updated with known rates λi. The cache downloads and keeps the freshest version of the files from the source with rates ci. The user gets updates from the cache with rates ui. When the user gets an update, it either gets a fresh update from the cache or the file at the cache becomes outdated by a file update at the source in which case the user gets an outdated update. We find an analytical expression for the average freshness of the files at the user. Next, we generalize our setting to the case where there are multiple caches in between the source and the user, and find the average freshness at the user. We provide an alternating maximization based method to find the update rates for the cache(s), ci, and for the user, ui, to maximize the freshness of the files at the user. We observe that for a given set of update rates for the user (resp. for the cache), the optimal rate allocation policy for the cache (resp. for the user) is a threshold policy, where the optimal update rates for rapidly changing files at the source may be equal to zero. Finally, we consider a system where multiple users are connected to a single cache and find update rates for the cache and the users to maximize the total freshness over all users.

We consider an information updating system where a source produces updates as requested by a transmitter. The transmitter further processes these updates in order to generate partial updates, which have smaller information compared to the original updates, to be sent to a receiver. We study the problem of generating partial updates, and finding their corresponding real-valued codeword lengths, in order to minimize the average age experienced by the receiver, while maintaining a desired level of mutual information between the original and partial updates. This problem is NP hard. We relax the problem and develop an alternating minimization based iterative algorithm that generates a pmf for the partial updates, and the corresponding age-optimal real-valued codeword length for each update. We observe that there is a tradeoff between the attained average age and the mutual information between the original and partial updates.

An information source generates independent and identically distributed status update messages from an observed random phenomenon which takes n distinct values based on a given pmf. These update packets are encoded at the transmitter to be sent to a receiver which wants to track the observed random variable with as little age as possible. The transmitter implements a selective k encoding policy such that rather than encoding all possible n realizations, the transmitter encodes the most probable k realizations and sends a designated empty symbol when one of the remaining n-k realizations occurs. We consider two scenarios: when the empty symbol does not reset the age and when the empty symbol resets the age. We find the time average age of information and the age-optimal real codeword lengths, including the codeword length for the empty symbol, for both of these scenarios. Through numerical evaluations for arbitrary pmfs, we show that this selective encoding policy yields a lower age at the receiver than encoding every realization and find the corresponding age-optimal k values.

We consider an information update system where an information receiver requests updates from an information provider in order to minimize its age of information. The updates are generated at the transmitter as a result of completing a set of tasks such as collecting data and performing computations. We refer to this as the update generation process. We model the quality (i.e., distortion) of an update as an increasing (resp. decreasing) function of the processing time spent while generating the update at the transmitter. While processing longer at the transmitter results in a better quality (lower distortion) update, it causes the update to age. We determine the age-optimal policies for the update request times at the receiver and update processing times at the transmitter subject to a minimum required quality (maximum allowed distortion) constraint on the updates.