Software aging, caused by the accumulation of errors and depletion of system resources, degrades the performance of long-running software systems and increases their failure risk. Software rejuvenation alleviates this effect by periodically restoring the system state, and existing rejuvenation strategies are commonly classified as time-based or condition-based. Time-based rejuvenation is easy to implement but lacks adaptability to evolving degradation, whereas condition-based rejuvenation improves efficiency at the expense of frequent inspections and increased operational cost. To overcome these limitations, this paper proposes a hybrid rejuvenation policy that combines scheduled rejuvenation with state-dependent inspections. Under a unified Markovian aging-failure-repair model, we analytically evaluate time-based, condition-based, and hybrid rejuvenation policies using a common stochastic framework. Closed-form expressions for steady-state availability, user-perceived availability, and expected operational cost are derived. Numerical experiments demonstrate that the hybrid policy achieves a more favorable availability-cost tradeoff by retaining the simplicity of time-based rejuvenation while incorporating the adaptive features of condition-based control.

This study investigates the platoon formation problem for autonomous trucks, in which vehicles accumulate at a staging station prior to entering the highway. Although platooning reduces aerodynamic drag and improves fuel efficiency—with larger platoons providing greater energy savings—it also increases inter-departure intervals, potentially compromising service frequency and schedule reliability. To address this trade-off, we analyze a dual-threshold (T, N) policy: a platoon departs either when the maximum waiting time T since the first vehicle’s arrival is reached, or when the number of waiting vehicles reaches the target size N. We derive explicit expressions for the resulting platoon size, waiting time, and inter-departure intervals, as well as the expected per-vehicle energy consumption. Numerical experiments under diverse traffic scenarios demonstrate that the (T, N) policy achieves significant energy savings while ensuring operational stability through controlled departure intervals. These results indicate that the (T, N) policy offers a robust and practical framework for the early deployment of autonomous truck platooning systems.

Recent technological development allows a queue of vehicles to be driven safely close to each other, which increases road utilization and reduces air drag, thus, resulting in significant energy savings. The queue of vehicles that follow one another in close succession is called a vehicle platoon. In the early stages of connected autonomous vehicles (CAVs) platooning, CAVs are expected to form platoons at their departure point according to an appropriate platoon formation policy. However, the effect of platoon formation policy on traffic capacity is rarely considered. This paper analyzes the effect of platoon formation policy and platoon size on the capacity of mixed traffic flow with CAVs, autonomous vehicles, and human-driven vehicles. First, given platoon size distribution, we derive the probability mass function for the position of an arbitrary CAV within a platoon and obtain mixed traffic capacity as a function of CAV penetration rate and average platoon size. The platoon size is heavily influenced by platoon formation policies. So, the platoon size distributions are derived for several platoon formation policies and are applied to obtain the mixed traffic capacities under the platoon formation policies. Some numerical examples are also provided to demonstrate how the key parameters of platoon formation policies affect the mixed traffic capacity.

This paper considers a Geo/G/1 queueing system within a discrete-time framework. The model seamlessly integrates state-dependent policies, incorporating both single working vacation and multiple vacations, thereby reflecting the dynamic nature of telecommunication environments. The matrix analytic method is utilized to analyze essential system performance indices, such as long-run probabilities of the distinct server states and the expected queue size of the system, offering insights into the nuanced behavior of Geo/G/1 queueing systems within the discrete-time framework. The results are expected to offer valuable insights for enhancing the performance of telecommunication networks. These insights cover various aspects, including single working vacations, multiple vacations, and state-dependent policies. Consequently, they are poised to establish a solid foundation for improving system efficiency and adapting to dynamic operational conditions.

Incorporating N-Limited working repairs ensures the uninterrupted forwarding of packets for some time in the event of a processor failure. This mechanism is applied to Geo/Geo/1 queueing systems characterized by state-dependent arrival and service rates. Employing matrix geometric analysis, we delve into the exploration of the steady-state distribution, accounting for state-dependent service times. The server may encounter breakdowns, yet, during repairs, the system maintains packet forwarding for the subsequent N customers. We derive equilibrium conditions and scrutinize the steady-state distribution of the system state and the number of customers in the system. This study contributes to understanding the implications of N-limited working repairs on the average number of customers in Geo/Geo/1 queues governed by state-dependent characteristics.

The graceful restart mechanism, integrated into network equipment to minimize packet loss during management system failures, is vitasl for maintaining service continuity. This functionality enables uninterrupted packet transmission for a predefined time interval following a processor failure, preventing system disruptions. In this study, we investigate a queuing system with graceful restart, emphasizing service persistence. We introduce a stability condition using matrix geometric analysis to examine the stationary distribution of both the number of customers and the system state. Furthermore, we analyze performance metrics, including the mean number of customers and the mean delay, and provide numerical examples. This research enhances our understanding of queuing systems and offers insights for optimizing systems with graceful restart mechanisms.

A vehicle platoon is a group of vehicles that can travel very close to each other safely at high speed. This paper deals with a system in which vehicles arrive at a station according to a Poisson process. Longer platoons are preferred when minimizing energy consumption, as the more vehicles in the platoon, the lower the total energy consumption. However, forming long platoons increases transport delay as vehicles have to wait longer. We consider a platoon formation policy with a time limit, time-limited policy: Platoon formation process begins with vehicles arriving when the station is empty; It lasts until an exact predetermined time limit has passed. This paper analyzes the platoon size and the energy consumption.

In this paper, we study real-time error in the context of monitoring a binary information source through a delay system. To derive the average real-time error, we model the delay system as a discrete time Geo/D/1/1 queueing model. Using a discrete time three-dimensional Markov chain with finite state space, we analyze the queueing model. We also perform some numerical analysis on various system parameters: state transition probabilities of binary information source; transmission times; and transmission frequencies. When the state changes of the information source are positively correlated and negatively correlated, we investigate the relationship between transmission time and transmission frequency.

The age of information (AoI) was proposed to quantify the freshness of information about the status of a remote source system, which is defined as the amount of time that has elapsed since a packet was created at its source. This paper analyzes the age of information of a discrete time Geo/D/1/1 status update system. For this purpose, the system is modeled as a discrete-time two-state Markov chain. The stationary probability distributions for peak AoI and AoI are obtained. The average peak AoI, the average AoI, and the freshness ratio of information are also derived. Some numerical results of the analysis are presented.

We consider a queueing system in which the server does not stop immediately after breakdowns but keeps working for a limited period of time. Many physical real-life situations can be more accurately analyzed by this kind of queueing systems. For example, it can be used to model nonstop forwarding mechanism applied to network equipment, which allows networking applications to continue forwarding their packets even in the event of a network failure. Within the framework of M/M/1 time-limited nonstop forwarding queue, we derive analytically the service availability, the steady-state joint distribution of the system state and the number of customers, and the delay distribution by using probability generating function method. Some numerical examples are also presented to demonstrate the applicability of the queueing systems with nonstop forwarding.

The age of information is the time elapsed since the generation of the last successfully received update message. In this Letter, the authors propose a new metric, freshness ratio of information (FRoI), defined as the fraction of time the age does not exceed a predefined freshness threshold. In addition, they analyse the FRoI for two different system models.

We consider a checkpointing model for silent errors, where a checkpoint is taken every fixed number of verifications. Assuming generally distributed i.i.d. inter-occurrence times of errors, we derive the reliability of the model as a function of the number of verifications between two checkpoints and the duration of work interval between two verifications.

54 www.ijeas.org Abstract— This paper deals with a Markovian queueing system, where the system can fail partially, fail completely, or be shutdown for preventive maintenance. The partially failed system can fail completely, or be shutdown for preventive maintenance. When completely failed, the system is repaired. The system works as new after preventive maintenance or repair. The steady-state availability is analized analytically and some numerical results are given.

This paper presents the analysis of the three parallel triplicated redundancy models: model with one active and two standby components, model with one standby and two active components, and model with three active components. The time-to-failure and the time-to-repair of the components follow an exponential and a general distribution, respectively. The repairs of failed components are randomly interrupted. The time-to-interrupt is taken from an exponentially distributed random variable and the interrupt times are generally distributed. Using the supplementary variable method and integro-differential equations, we obtain the analytical expression of the availability for the redundancy models with imperfect switchovers and interrupted repairs. Numerical examples show the effect of failure rate of active components, repair interruption rate, and switchover failure probability on the steady-state availability. The triplicated redundancy model with one active component and two standby components has higher availability than the other triplicated models with more active components when the switchover failure probability is small.

This paper considers the design and analysis of a discrete-time GeoX/D/c/Nnbspqueueing system with batch geometric arrivals, multiple servers, and retention of reneging customers. This paper derives the limiting probability distribution of the number of customers in the system and also obtains the expression for the proportion of arriving customers that are blocked.

This paper considers a discrete-time Geo^x/D/queueing system where customers arrive at a facility with a single server according to a batch geometric process with customer service times assumed to be one slot. This paper investigates the mean excess over a threshold for the number of customers in the queueing system.

Consider a classical discrete-time single server queueing system, consisting of a stream of customers arriving according to a batch geometric process and a server that processes these customers with deterministic service time of slot. The random variable is defined as the number of customers in the queueing system at the -th slot boundary. Let be the slot boundary of first entry into the interval , , of the number of customers. The distribution of the excess at the first-passage time over the threshold for the number of customers is defined as

This paper considers a discrete-time queueing system with batch geometric arrivals and retention of reneging customers, in which retention probability depends on the number of customers in the system. The steady state probability distribution of the number of customers in the system is derived. Other performance measures such as mean number of customers in the system, blocking probability, abandon probability, and service completion probability are obtained. Numerical examples are also given.