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Tail decay of the M|M|1 queue. Bounds compared to exact results. For update interval w ≈ 1 the age is minimal.
Source publication
This paper contributes tail bounds of the age-of-information of a general class of parallel systems and explores their potential. Parallel systems arise in relevant cases, such as in multi-band mobile networks, multi-technology wireless access, or multi-path protocols, just to name a few. Typically, control over each communication channel is limite...
Context in source publication
Context 1
... we showed results for parallel M|M|1 queues already in Fig. 3, we only add numerical results that evaluate the accuracy of the bound. Fig. 6 shows the tail bound compared to the exact tail decay of the M|M|1 queue. Compared to the results for the M|D|1 queue in Fig. 5, it can be noticed that the bounds for the M|M|1 queue are slightly looser if w is small. This is due to the use of Def. 1 that specifies samplepath envelopes for the arrivals and for the service separately, ...
Citations
... The concept of AoI was initially defined in the field of vehicular communications [1] and motivated the investigation of AoI in queueing systems [2]. Today, the AoI is known for a variety of system models, see the recent surveys [3], [4], including wireless channels [5], [6], wireless networks [7], random access channels [8]- [10], queueing systems [11], [12], and queueing networks [13]. While the focus has been on mean AoI and mean peak AoI, there are a number of papers that derive the CCDF [12], [14], [15] or tail bounds of the AoI [16], [17]. ...
... Markovian and deterministic queues with feedback. Directly related to multi-sensor systems that observe a single physical phenomenon are parallel systems in which the samples from a single sensor are split between two (or more) independent channels [6], [50]. As only the most recent sample is decisive for the AoI, the main characteristic of parallel systems is that their AoI is the minimum of the AoI of the individual subsystems. ...
... AoI. This provides a direct link to the AoI literature, where our result generalizes the AoI of parallel systems [6], [50] by considering correlated spatio-temporal processes instead of a single temporal process. ...
The freshness of sensor data is critical for all types of cyber-physical systems. An established measure for quantifying data freshness is the Age-of-Information (AoI), which has been the subject of extensive research. Recently, there has been increased interest in multi-sensor systems: redundant sensors producing samples of the same physical process, sensors such as cameras producing overlapping views, or distributed sensors producing correlated samples. When the information from a particular sensor is outdated, fresh samples from other correlated sensors can be helpful. To quantify the utility of distant but correlated samples, we put forth a two-dimensional (2D) model of AoI that takes into account the sensor distance in an age-equivalent representation. Since we define 2D-AoI as equivalent to AoI, it can be readily linked to existing AoI research, especially on parallel systems. We consider physical phenomena modeled as spatio-temporal processes and derive the 2D-AoI for different Gaussian correlation kernels. For a basic exponential product kernel, we find that spatial distance causes an additive offset of the AoI, while for other kernels the effects of spatial distance are more complex and vary with time. Using our methodology, we evaluate the 2D-AoI of different spatial topologies and sensor densities.
... [12] studies the age-delay trade-off in G/G/∞ queue. [13] observes that a single M/M/1 queue has better age performance than the independent parallel M/M/1 queues with the same total capacity. [14] analyzed age in network of parallel finite identical and memoryless servers, where each server is an LCFS queue with preemption in service. ...
This work explores systems where source updates require multiple sequential processing steps. We model and analyze the Age of Information (AoI) performance of various system designs under both parallel and series server setups. In parallel setups, each processor executes all computation steps with multiple processors working in parallel, while in series setups, each processor performs a specific step in sequence. In practice, processing faster is better in terms of age but it also consumes more power. We identify the occurrence of wasted power in these setups, which arises when processing efforts do not lead to a reduction in age. This happens when a fresher update finishes first in parallel servers or when a server preempts processing due to a fresher update from preceding server in series setups. To address this age-power trade-off, we formulate and solve an optimization problem to determine the optimal service rates for each processing step under a given power budget. We focus on a special case where updates require two computational steps.
... The results showed that the average AoI performance of the systems in [26]- [29] was significantly improved compared with corresponding single queue systems. The authors of [30] derived the statistical AoI bounds for a broad class of parallel systems. ...
... where (h) follows from (28), (30), and (27) . Combining (28), (30) and (31), it has that for q ∈ Q, ...
... where (h) follows from (28), (30), and (27) . Combining (28), (30) and (31), it has that for q ∈ Q, ...
Timely status updating is the premise of emerging interaction-based applications in the Internet of Things (IoT). Using redundant devices to update the status of interest is a promising method to improve the timeliness of information. However, parallel status updating leads to out-of-order arrivals at the monitor, significantly challenging timeliness analysis. This work studies the Age of Information (AoI) of a multi-queue status update system where multiple devices monitor the same physical process. Specifically, two systems are considered: the Basic System, which only has type-1 devices that are ad hoc devices located close to the source, and the Hybrid System, which contains additional type-2 devices that are infrastructure-based devices located in fixed points compared to the Basic System. Using the Stochastic Hybrid Systems (SHS) framework, a mathematical model that combines discrete and continuous dynamics, we derive the expressions of the average AoI of the considered two systems in closed form. Numerical results verify the accuracy of the analysis. It is shown that when the number and parameters of the type-1 devices/type-2 devices are fixed, the logarithm of average AoI will linearly decrease with the logarithm of the total arrival rate of type-2 devices or that of the number of type-1 devices under specific condition. It has also been demonstrated that the proposed systems can significantly outperform the FCFS M/M/N status update system.
... Update Q(s, a) according to (21) 8: end for 9: If every element in |Q(s, a) − Q c (s, a)| ≤ α, c ←− c + 1. 10: If c = 10, go to the next step. Otherwise, ϵ ←− max(0.01, ...
In heterogeneous wireless networked control systems (WNCSs), the age of information (AoI) of the actuation update and actuation update cost are important performance metrics. To reduce the monetary cost, the control system can wait for the availability of a WiFi network for the actuator and then conduct the update using a WiFi network in an opportunistic manner, but this leads to an increased AoI of the actuation update. In addition, since there are different AoI requirements according to the control priorities (i.e., robustness of AoI of the actuation update), these need to be considered when delivering the actuation update. To jointly consider the monetary cost and AoI with priority, this paper proposes a priority-aware actuation update scheme (PAUS) where the control system decides whether to deliver or delay the actuation update to the actuator. For the optimal decision, we formulate a Markov decision process model and derive the optimal policy based on Q-learning, which aims to maximize the average reward that implies the balance between the monetary cost and AoI with priority. Simulation results demonstrate that the PAUS outperforms the comparison schemes in terms of the average reward under various settings.
... To address the AoI control problem in heterogeneous networks, there have been several works [13][14][15][16][17][18]. Pan et al. [13] determined the scheduling policy over an unreliable but fast channel or a slow reliable channel to minimize AoI. ...
... Bhati et al. [16] provided the optimal average AoI considering heterogeneous multiple servers with different capabilities. Fidler et al. [17] showed the effect of independent parallel channels on AoI based on the queuing models. Xie et al. [18] formulated the generalized scheduling problem in multi-sensor multi-server systems to minimize AoI. ...
... In Figure 6b, it can be noted that PAUS cannot guarantee the AoI requirement at higher C m . This is because PAUS reduces the monetary cost at higher C m , which can increase AoI, to maximize the total reward function defined in (17). Note that if the system operator needs to enhance AoI satisfaction ratio even at higher C m , the weight factor w in the total reward function can be adjusted. ...
In the heterogeneous wireless networked control system (WNCS), age of information (AoI) of the actuation update and actuation update cost are important performance metrics. To reduce the monetary cost, the control system can wait for the availability of WiFi network of the actuator and then conduct the update by using WiFi network in an opportunistic manner, but it leads to the increased AoI of the actuation update. To assess this problem, this paper proposes a priority-aware actuation update scheme (PAUS) where the control system decides whether to deliver or delay the actuation update to the actuator by considering the control priority (i.e., robustness of AoI of the actuation update). For the optimal decision, we formulate a Markov decision process model and derive the optimal policy based on Q-learning. Simulation results demonstrate that PAUS outperforms the comparison schemes in terms of the expected reward.
Timely status updating is the premise of emerging interaction-based applications in the Internet of Things (IoT). Using redundant devices to update the status of interest is a promising method to improve the timeliness of information. However, parallel status updating leads to out-of-order arrivals at the monitor, significantly challenging timeliness analysis. This work studies the Age of Information (AoI) of a multi-queue status update system where multiple devices monitor the same physical process. Specifically, two systems are considered: the
Basic System
, which only has type-1 devices that are ad hoc devices located close to the source, and the
Hybrid System
, which contains additional type-2 devices that are infrastructure-based devices located in fixed points compared to the
Basic System
. Using the Stochastic Hybrid Systems (SHS) framework, a mathematical model that combines discrete and continuous dynamics, we derive the expressions of the average AoI of the considered two systems in closed form. Numerical results verify the accuracy of the analysis. It is shown that when the number and parameters of the type-1 devices/type-2 devices are fixed, the logarithm of average AoI will linearly decrease with the logarithm of the total arrival rate of type-2 devices or that of the number of type-1 devices under specific condition. It has also been demonstrated that the proposed systems can significantly outperform the FCFS M/M/
N
status update system.
