The self-adaptive routing strategy to alleviate packet loss in finite buffer networks

In real communication or transportation systems, loss of agents is very common due to finite storage capacity. We study the traffic dynamics in finite buffer networks and propose a routing strategy motivated by a heuristic algorithm to alleviate packet loss. Under this routing strategy, the traffic capacity is further improved, comparing to the shortest path routing strategy and efficient routing strategy. Then we investigate the effect of this routing strategy on the betweenness of nodes. Through dynamic routing changes, the maximum node betweenness of the network is greatly reduced, and the final betweenness of each node is almost the same. Therefore, the routing strategy proposed in this paper can balance the node load, thereby effectively alleviating packet loss.

Analysis of Energy Efficient Scheduling of the Manufacturing Line with Finite Buffer Capacity and Machine Setup and Shutdown Times

The aim of this paper is to present a model of energy efficient scheduling for series production systems during operation, including setup and shutdown activities. The flow shop system together with setup, shutdown times and energy consumption are considered. Production tasks enter the system with exponentially distributed interarrival times and are carried out according to the times assumed as predefined. Tasks arriving from one waiting queue are handled in the order set by the Multi Objective Immune Algorithm. Tasks are stored in a finite-capacity buffer if machines are busy, or setup activities are being performed. Whenever a production system is idle, machines are stopped according to shutdown times in order to save energy. A machine requires setup time before executing the first batch of jobs after the idle time. Scientists agree that turning off an idle machine is a common measure that is appropriate for all types of workshops, but usually requires more steps, such as setup and shutdown. Literature analysis shows that there is a research gap regarding multi-objective algorithms, as minimizing energy consumption is not the only factor affecting the total manufacturing cost—there are other factors, such as late delivery cost or early delivery cost with additional storage cost, which make the optimization of the total cost of the production process more complicated. Another goal is to develop previous scheduling algorithms and research framework for energy efficient scheduling. The impact of the input data on the production system performance and energy consumption for series production is investigated in serial, parallel or serial–parallel flows. Parallel flow of upcoming tasks achieves minimum values of makespan criterion. Serial and serial–parallel flows of arriving tasks ensure minimum cost of energy consumption. Parallel flow of arriving tasks ensures minimum values of the costs of tardiness or premature execution. Parallel flow or serial–parallel flow of incoming tasks allows one to implement schedules with tasks that are not delayed.

Study on Transient Queue-Size Distribution in the Finite-Buffer Model with Batch Arrivals and Multiple Vacation Policy

The transient behavior of the finite-buffer queueing model with batch arrivals and generally distributed repeated vacations is analyzed. Such a system has potential applications in modeling the functioning of production systems, computer and telecommunication networks with energy saving mechanism based on cyclic monitoring the queue state (Internet of Things, wireless sensors networks, etc.). Identifying renewal moments in the evolution of the system and applying continuous total probability law, a system of Volterra-type integral equations for the time-dependent queue-size distribution, conditioned by the initial buffer state, is derived. A compact-form solution for the corresponding system written for Laplace transforms is obtained using an algebraic approach based on Korolyuk’s potential method. An illustrative numerical example presenting the impact of the service rate, arrival rate, initial buffer state and single vacation duration on the queue-size distribution is attached as well.

Asymptotic Analysis for Systems with Deferred Abandonment

This short paper concerns the analysis of the M/M/k queueing system with customer abandonment. In this system, service managers provide a finite buffer space, which is a waiting area that prevents customers from abandoning the system. Abandonment of the system can occur from reneging (exiting from the queue while waiting), and/or balking (leaving the system without waiting). We derive an analytical expression to represent the impact of the buffer space capacity on the delay probability and the abandonment probability for a system with deferred abandonment. The result indicates the provision of the buffer space in a large system could only increase the delay probability while the abandonment probability remains unchanged. Despite the benevolent intentions of service managers, providing a buffer space may exacerbate the performance of larger systems.

Modelling customers’ impatience with discouraged arrival and retention of reneging

This paper presents stochastic modelling of a single server, finite buffer Markovian queuing system with discouraged arrivals, balking, reneging, and retention of reneged customers. Markov process is used to derive the steady-state solution of the model. Closed form expressions using probability generating functions (PGFs) are derived and presented for both classical and novel performance measures. In addition, a sensitivity analysis is carried out to study the effect of the system parameters on performance measures. A numerical problem is also presented to demonstrate the derived results and some design aspects.

Eulerian polynomials and Quasi-Birth-Death processes with time-varying-periodic rates

A Quasi-Birth-Death (QBD) process is a stochastic process with a two dimensional state space, a level and a phase. An ergodic QBD with time-varying periodic transition rates will tend to an asymptotic periodic solution as time tends to infinity . Such QBDs are also asymptotically geometric. That is, as the level tends to infinity, the probability of the system being in state ( k , j ) (k,j) at time t t within the period tends to an expression of the form f j ( t ) α − k Π j ( k ) f_j(t)\alpha ^{-k}\Pi _j(k) where α \alpha is the smallest root of the determinant of a generating function related to the generating function for the unbounded (in the level) process, Π j ( k ) \Pi _j(k) is a polynomial in k k , the level, that may depend on j j , the phase of the process, and f j ( t ) f_j(t) is a periodic function of time within the period which may also depend on the phase. These solutions are analogous to steady state solutions for QBDs with constant transition rates. If the time within the period is considered to be part of the state of the process, then they are steady-state solutions. In this paper, we consider the example of a two-priority queueing process with finite buffer for class-2 customers. For this example, we provide explicit results up to an integral in terms of the idle probability of the queue. We also use this asymptotic approach to provide exact solutions (up to an integral equation involving the probability the system is in level zero) for some of the level probabilities.