Information freshness is one of the critical aspects of communication networks. Average age of information (AoI) and peak AoI (PAoI) are the main metrics for evaluating information freshness. Modeling the communication system with a stochastic hybrid system (SHS) is an effective approach for finding these metrics, especially in complex network scenarios. A regular SHS is comprised of a Markov chain (MC) and some stochastic processes evolving according to the state of the MC. The Markovian property of the chain in regular SHSs limits the capability of this approach in analyzing general network scenarios, e.g., when the transmission times of packets follow a general non-exponential distribution. In this work, we focus on the semi-Markovian-SHSs (SM-SHSs). In SM-SHSs, compared to regular SHSs, the Markovian property of the system chain is extended to semi-Markovian property, i.e., the sojourn time in each state follows an arbitrary distribution depending on the next transition in the system chain. We derive theorems for finding the average AoI and PAoI when the communication system is modeled with an SM-SHS. We also propose an age-ordering-aware multi-stream M/G/1/1 queueing system with the assumption of deterministic vacation times for the server and analyze this system using the SM-SHS approach.

In this paper, we study the information freshness in a network with two information classes, where class 1 packets have a priority higher than class 2 packets. We propose a new queueing policy with delayed preemptions, that is, when a class 1 packet arrives while a class 2 packet is in service, instead of the usual immediate preemption, a deadline is assigned for the service of class 2 packets. By the end of the mentioned deadline, if the low-priority packet is still in service, it is preempted. The main goal of this delayed preemption policy is to balance the freshness metrics of the information classes, which is an intrinsic attribute in some applications, e.g., caching of dynamic contents, where the freshness of some contents is more critical than the others. For exponentially distributed deadlines, by exploiting a stochastic hybrid system (SHS), we evaluate the average age of information (AoI) and average peak AoI (PAoI). We also find general formulas for the average PAoIs of the classes for arbitrarily distributed deadlines and use them to find the average PAoI for deterministic deadlines. By numerical results, we investigate the performance of this policy in balancing the average AoIs/PAoIs of information classes.

In this paper, we study the age of information (AoI) in a network consisting of multiple information streams with different priorities sharing a common server. In this network, the transmission of a packet is interrupted whenever a higher priority packet arrives. Regarding the behavior of AoI, for each stream, we consider a single buffer to enqueue the incoming packets based on a quasi-blocking (QB) policy. With the assumption of Poisson packet arrivals, we formulate the AoI and PAoI moment generating functions for each stream, while no assumption is considered for the service times of the packets. We also introduce a new semantic queueing policy. In this respect, we define the semantic (i.e., significance) of a packet as a linear combination of its age and remaining transmission time. When this metric is lower for a packet, the packet is more significant. In this policy, the decision to replace the available packet of a stream with a new arriving one is made based on the significance of these packets. This decision minimizes the sum of the next local peak and end-to-end delay in the AoI function. We investigate the superiority of this policy to the traditional ones in our numerical results.

In this work, we study the age of information (AoI) in a multi-hop multi-path network with$r$distinct independent paths from the source to the destination. Each path is considered as a tandem network consisting of$k$preemptive servers. We consider two different policies for choosing a path to transmit a packet. In the first policy, each packet is randomly assigned to only one path. In the second one, each packet is assigned to all of the paths. In both policies, packets may be delivered out-of-order, which makes the AoI analysis challenging. To overcome this challenge, we exploit the age of link (AoL) concept which enables us to study AoI in multi-path systems. Then, we use a stochastic hybrid system (SHS) approach for finding the average AoI. In the symmetric case where the service rates of the servers are equal, we find a lower-bound on the average AoI, which shows increasing the number of paths is not effective when the number of hops is relatively large.

In this paper, we analyze the effect of implementing variable backoff algorithms on the average peak age of information (PAoI) and the average age of information (AoI) in slotted ALOHA networks. To this end, we first analytically derive the average PAoI in exponential backoff slotted ALOHA when the number of backoff stages is finite. We also show that the reduction in average PAoI achieved by the exponential backoff algorithm can significantly increase the average AoI, which is not desirable. Then, we propose an age-based backoff algorithm and present the intuition behind it. In contrast to exponential backoff, our proposed age-based backoff algorithm reduces the average PAoI significantly, while changing the average AoI limitedly. The numerical results confirm our analytical results as well as the superiority of the proposed age-based backoff algorithm over exponential backoff.

In this paper, we concentrate on the peak age of information (PAoI) in a discrete-time slotted ALOHA network comprised of$\boldsymbol {M}$buffer-less nodes, capable of keeping just one packet at each slot. In this network, a collision happens whenever at least two nodes transmit their packets simultaneously. Thus, there is some interaction among queues, and the transmission delay of a packet might prolong more than one slot. The packets are generated at each node stochastically and independently. The nodes follow the preemptive queueing policy. In this network, we propose a trellis-based model to analyze packet system time and derive the exact average PAoI of symmetric and asymmetric slotted ALOHA networks. We confirm our analysis by simulation results in different conditions. By exploiting numerical results, we optimize the average PAoI of the symmetric slotted ALOHA network, find the PAoI-constrained regions, and compare the PAoI of slotted ALOHA networks with and without retransmission of the failed packets.