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.

ON TIME-TO-BUFFER OVERFLOW DISTRIBUTION IN A SINGLE-MACHINE DISCRETE-TIME SYSTEM WITH FINITE CAPACITY

A model of a single-machine production system with finite magazine capacity is investigated. The input flow of jobs is organized according to geometric distribution of interarrival times, while processing times are assumed to be generally distributed. The closed-form formula for the generating function of the time to the first buffer overflow distribution conditioned by the initial buffer state is found. The analytical approach based on the idea of embedded Markov chain, the formula of total probability and linear algebra is applied. The corresponding result for next buffer overflows is also given. Numerical examples are attached as well.

Optimal Design and Operation of Buffer Tanks Under Stochastic Conditions

Safety regulations demand the elimination of random mistakes and the reliable operation of production units. However, the control and maintenance of batch and semi-continuous processes haalways been difficult. In this paper, a way of preventing malfunctions in batch and semi-continuous processes is presented by using appropriately designed buffer tanks. A stochastic model was investigated in which batch and continuous subsystems were linked by an intermediate storage tank. The main concern was the reliability of the system. Reliable operation was defined as neither the exhaustion of raw materials nor the excessive accumulation of them. The counting processes that describe the random batch-input and random batch-output processes are supposed to be independent homogeneous Poisson processes with different rates. By introducing a function that describes the material in storage, reliable operation is defined as when this function satisfies two inequalities for a time interval of any duration. By applying probabilistic methods, an integral equation is set up for the the reliability. Nevertheless, its analytical solution cannot be determined, hence the values according to a Monte Carlo simulation are approximated. By applying this method, a link could be identified between the necessary initial buffer and tank capacities that belong to a reliability level. Economic investigations were conducted to help determine the optimal initial buffer and tank capacities that satisfy the appointed reliability level.

The Future Defense System for the Indonesian Nation State

The curent global situation has encouraged inter-state rivalry to become increasingly violent, so that the survival of every nation-state is becoming increasingly vulnerable. Therefore, every nation state has a responsibility to develop its own defense system to deal with the physical and psychological threats. This paper discusses the challenges and concepts of future defense system for the Indonesia, with the framework of analysis is the security vortex. The concept of the future defense system for the nation state of Indonesia is concentric defense, which consists of internal and external defense belt, by building three basic capabilities of the TNI to ensure national security, and to build global strategic partnership, which put Indonesia as an initial buffer of regional stability.

Replication Placement on Disks

When extra storage space is available on the striping disks being described in the last chapter, the storage system may keep extra copies of the stored objects to enhance the performance of the storage system. If any one of the copy or the original copy is corrupted, the corrupted copy can possibly be recovered by comparison with its replicas. The replication strategy thus increases reliability of the storage system by applying redundancy on the stored objects. Extra copies of objects may be created and stored on the storage system to increase the storage system performance. The presence of replicas on light loading disks may be able to reduce the period of time that an object is inaccessible. Thus, the replication strategy increases the availability of the stored objects. The replication strategy can have several advantages. First, the replica on idle disks can increase the availability of data on corrupted and busy disks. Second, the replica on local server can reduce the network load to access objects from remote servers. Third, the replica on local server can also reduce the need to wait for the filling of initial buffer prior to consumption. Fourth, replica can avoid disk multitasking by avoiding the need to serve multiple streams from the same disk head. We will describe the streaming redundant array of inexpensive disks (RAID) method that increases availability and fault tolerance in the next section. After that, we present the Lancaster storage server to reduce network load. Then, we show two data replication methods to reduce start-up latency. Afterwards, we explain how the data replication method can avoid disk multitasking. Before we conclude this chapter, we describe the replication method that balances the space and workload of storage devices.

OPTIMAL ATTRACTORS AND SWITCHED KANBAN CONTROL IN DISCRETE STRANGE BILLIARDS

Switched buffer systems are discretized switched flow systems. They are discrete, but can be handled with the same mathematical framework as hybrid systems. In particular, we show that switched buffer systems form discrete strange billiards. For any initialization, discrete strange billiards lead to a finite periodic attractor. The periods and the buffer switching rates are the most important performance measures for the practical use of switched buffer systems. Both measures depend on the sum of objects in the buffers. For each object sum multiple suboptimal attractors may exist. Onto which attractor the system converges depends on the initial buffer levels. We propose a switched Kanban control algorithm that forces the system onto the attractor with minimum buffer switching rate independently of the initialization of the buffer levels. This algorithm needs to perform only one single additional buffer switching operation. Also Heijunka control of switched buffer systems is considered in the framework of strange billiards. We show that Heijunka forms equilateral triangles in the state space. Heijunka is able to yield low buffer switching rates, but only if the buffer levels are optimally initialized. For suboptimal buffer level initializations very high (bad) buffer switching rates can be achieved. In an illustrative example, our proposed switched Kanban control algorithm outperforms conventional Kanban control by about 29% and Heijunka control by about 5%.