Arbitrary Arrival Times Research Articles

Sequencing in an appointment system with deterministic arrivals and non-identical exponential service times

This paper investigates an appointment system with deterministic arrival times and non-identical exponential service times with the objective of minimizing the expected costs of customer-waiting and server-idle times (WIT). For two customers, this paper shows analytically that the smallest-variance-first-rule (SV) and, equivalently, the smallest-mean-first-rule (SM) minimize WIT when the second customer arrives at either optimal or arbitrary arrival time. For three customers, this paper shows analytically that either SV or SM minimize WIT, assuming that each customer arrives at the cumulative sum of expected service times of prior customers. Based on numerical evaluation, this paper recommends that the exponential distribution parameter, which determines either SV or SM sequences, be used for a general number of customers.

Quantum-inspired ant colony optimisation algorithm for a two-stage permutation flow shop with batch processing machines

This paper studied two-stage permutation flow shop problems with batch processing machines, considering different job sizes and arbitrary arrival times, with the optimisation objective of minimising the makespan. The quantum-inspired ant colony optimisation (QIACO) algorithm was proposed to solve the problem. In the QIACO algorithm, the ants are divided into two groups: one group selects the largest job in terms of job size as the initial job for each batch and the other group selects the smallest job as the initial job for each batch. Each group of ants has its own pheromone matrix. In the computational experiment, our novel algorithm was compared with the hybrid discrete differential evolution (HDDE) algorithm and the batch-based hybrid ant colony optimisation (BHACO) algorithm. Although the HDDE algorithm has a shorter run time, the quality of the solution for large-scale jobs is not good, while the BHACO algorithm always obtains a better solution but requires a longer run time. The computational results show that the QIACO algorithm embedded in the quantum information has advantages in terms of both solution quality and running time.

Blind separation of partially overlapping data packets

The paper discusses the separation of partially overlapping data packets by an antenna array in narrowband communication systems. This problem occurs in asynchronous communication systems and several transponder systems such as Radio Frequency Identification (RFID) for wireless tags, Automatic Identification System (AIS) for ships, and Secondary Surveillance Radar (SSR) and Automatic Dependent Surveillance—Broadcast (ADS—B) for aircraft. Partially overlapping data packages also occur as inter-cell interference in mutually unsynchronized communication systems. Arbitrary arrival times of the overlapping packets cause nonstationary scenarios and makes it difficult to identify the signals using standard blind beamforming techniques. After selecting an observation interval, we propose subspace-based algorithms to suppress partially present (interfering) packets, as a preprocessing step for existing blind beamforming algorithms that assume stationary (fully overlapping) sources. The proposed algorithms are based on a subspace intersection, computed using a generalized singular value decomposition (GSVD) or a generalized eigenvalue decomposition (GEVD). In the second part of the paper, the algorithm is refined using a recently developed subspace estimation tool, the Signed URV algorithm, which is closely related to the GSVD but can be computed non-iteratively and allows for efficient subspace tracking. Simulation results show that the proposed algorithms significantly improve the performance of classical algorithms designed for block stationary scenarios in cases where asynchronous co-channel interference is present. An example on experimental data from the AIS ship transponder system confirms the effectiveness of the proposed algorithms in a real application.

Martian: Message Broadcast via LED Lights to Heterogeneous Smartphones

Visible light communication (VLC) has been shown to have several advantages over traditional wireless communication. In this paper, we envision an LED-light-to-smartphone VLC protocol for delivering messages to a group of randomly arriving smartphone receivers. Our goal is to increase the throughput for large message delivery, as well as to reduce the delay of message broadcast. Key challenges for implementing such a VLC message broadcast protocol are: 1) the imperfect synchronization among receivers and the transmitter; 2) the receivers’ arbitrary arrival times; and 3) the diversity of receivers’ smartphones (e.g., location, capability, and frame-rates). In this paper, we propose a new modulation scheme and design link-layer protocols for improving the network data rate. We carefully design and implement our protocol, Martian, which allows smooth communication from the LED lights to a group of smartphone embedded cameras. Across several phone models, Martian can achieve data rate of about 1.6 kb/s even with NLOS -light. It also has a stable and small delay for broadcasting messages to the randomly arriving receivers.

STOCHASTIC ANALYSIS OF PRINTED CIRCUIT BOARDS MANUFACTURING SYSTEM CONSIDERING REPAIRS BY INTERNAL/EXTERNAL ENGINEERS AND ARBITRARY ARRIVAL TIME OF EXTERNAL ENGINEERS

In the present paper, a stochastic model for the system involved in the printed circuit boards(PCBs) manufacturing process is developed. The manufacturing process, based on Surface Mount Technology (SMT), is carried out in three stages viz. printing, placing and soldering through a hardware-software system. During the process, inspections, maintenances and repairs on occurrence of faults of the system are done by internal/external engineers. The internal engineers inspect the system and every manufactured PCB. The system's software faults as well as faults in the PCBs are repaired by the internal engineers whereas system's hardware faults are repaired only by the external engineers. In the model, possibilities of different kinds of faults, online PCB's repairs and arbitrary arrival time of the external en- gineers, are also incorporated. The expressions for various measures of system performance have been derived using Markov process and regenerative techniques. In the last, numerical computation and graphical analysis have been given for a particular case to show the effect of various parameters on the system performance and cost-benefit.

Optimal energy efficient packet scheduling with arbitrary individual deadline guarantee

Given a rate adaptive wireless transmitter, a challenging problem is to design a rate control policy for it such that the energy consumption is minimized at transmitting a set of dynamically arrived packets with arbitrary individual deadlines. In a decade, researches have partially made progress on this topic. A latest work offers an optimal algorithm that allows packets to have arbitrary deadlines but requires them to follow the order they arrive. This paper first presents the Densest Interval First (DIF) policy which repeatedly locates the densest data interval and determines its transmission rate. This policy is proved to be optimal for the most general model that allows arbitrary arrival times as well as arbitrary deadlines. Then, this paper presents a simple EDF (earliest deadline first) algorithm to actually schedule the transmission time for each packet. It is proved that the EDF always guarantees every packet to complete transmission before its deadline with minimum energy consumption which is computed and required by DIF. Finally, this paper also proposes a novel online policy named Density Guided Cooling (DGC) policy which models Newton’s Law of Cooling. Simulations show that online DGC policy constantly produces a rate scheduling that on average consumes energy within 110% of the minimum value obtained by the offline DIF.

Optimal Server Selection in a Queueing Loss Model with Heterogeneous Exponential Servers, Discriminating Arrivals, and Arbitrary Arrival Times

We consider a multiple server queueing loss system where the service times of server i are exponential with rate μ i , where μ i decreases in i. Arrivals have associated vectors (X 1, …, X n ) of binary variables, with X i = 1 indicating that server i is eligible to serve that arrival. Arrivals finding no idle eligible servers are lost. Letting I j be the indicator variable for the event that the jth arrival enters service, we show that, for any arrival process, the policy that assigns arrivals to the smallest numbered idle eligible server stochastically maximizes the vector (I 1, …, I r ) for every r if the eligibility vector of arrivals is either (a) exchangeable, or (b) a vector of independent variables for which P(X i = 1) increases in i.

Optimal Server Selection in a Queueing Loss Model with Heterogeneous Exponential Servers, Discriminating Arrivals, and Arbitrary Arrival Times

We consider a multiple server queueing loss system where the service times of server i are exponential with rate μi, where μi decreases in i. Arrivals have associated vectors (X1, …, Xn) of binary variables, with Xi = 1 indicating that server i is eligible to serve that arrival. Arrivals finding no idle eligible servers are lost. Letting Ij be the indicator variable for the event that the jth arrival enters service, we show that, for any arrival process, the policy that assigns arrivals to the smallest numbered idle eligible server stochastically maximizes the vector (I1, …, Ir) for every r if the eligibility vector of arrivals is either (a) exchangeable, or (b) a vector of independent variables for which P(Xi = 1) increases in i.

Improved Schedulability Analysis of Real-Time Sporadic Tasks with EDF Preemptive Scheduling

This paper proposes an analysis method to check the schedulability of a set of sporadic tasks under earliest deadline first (EDF) scheduler. The sporadic task model consists of subtasks with precedence constraints, arbitrary arrival times and deadlines. In order to determine the schedulability, we present an approach to find exact worst case response time (WCRT) of subtatsks. With the technique presented in this paper, we exploit the precedence relations between subtasks in an accurate way while taking advantage of the deadline of different subtasks. Another nice feature of our approach is that it avoids calculation time overhead by exploiting the concept of deadline busy period. Experimental results show that this consideration leads to a significant improvement compared with existing work.

Optimal algorithms for single-machine scheduling with rejection to minimize the makespan

In this paper we consider the single-machine scheduling problem with rejection. Each job has an arrival time, a processing time and a rejection penalty. The objective is to minimize the sum of the makespan of the accepted jobs and the total rejection penalty of the rejected jobs. First, we present a polynomial-time algorithm for the off-line problem when split is allowed. Second, for the on-line problem with arbitrary arrival times, we provide a determined on-line algorithm with the best-possible competitive ratio 2. Finally, for the on-line problem with at most two distinct arrival times, we provide a determined on-line algorithm with the best-possible competitive ratio ( 5 + 1 ) / 2 ≈ 1.618 .

A Simple and Complete Solution to the Stationary Queue-Length Probabilities of a Bulk-Arrival Bulk-Service Queue

A complete solution for the stationary queue-length distribution of a bulk-arrival, bulk-service (GIX/MY/1) queue is presented. Beginning with a known expression for the probability generating function of the stationary pre-arrival-epoch queue-length distribution, the roots method is used to invert it and determine all probabilities. Next, using level crossing arguments, theoretical relationships between pre-arrival and arbitrary-epoch probabilities are developed. These relationships are then used to directly determine a complete set of probabilities for the arbitrary- epoch queue-length distribution. Finally, selected examples are presented. These demonstrate how, given arbitrary arrival time, arrival group size and service batch size probability distributions, a complete solution for the stationary queue-length probabilities can be readily determined.

Competitive online scheduling of perfectly malleable jobs with setup times

We study how to efficiently schedule online perfectly malleable parallel jobs with arbitrary arrival times on m ⩾ 2 processors. We take into account both the linear speedup of such jobs and their setup time, i.e., the time to create, dispatch, and destroy multiple processes. Specifically, we define the execution time of a job with length p j running on k j processors to be p j / k j + ( k j − 1) c, where c > 0 is a constant setup time associated with each processor that is used to parallelize the computation. This formulation accurately models data parallelism in scientific computations and realistically asserts a relationship between job length and the maximum useful degree of parallelism. When the goal is to minimize makespan, we show that the online algorithm that simply assigns k j so that the execution time of each job is minimized and starts jobs as early as possible has competitive ratio 4( m − 1)/ m for even m ⩾ 2 and 4 m/( m + 1) for odd m ⩾ 3. This algorithm is much simpler than previous offline algorithms for scheduling malleable jobs that require more than a constant number of passes through the job list.

Aggressor alignment for worst-case crosstalk noise

In this paper, we study signal alignment resulting in maximum peak interconnect coupling noise. We consider three cases. In the first one, we assume that arbitrary arrival times of input signals are feasible. In the second case, we assume that timing windows are given for each aggressor input. The victim is quiet for the above two cases. In the third case, the victim net has a propagated noise from the previous stage and timing windows are given for both the propagating noise and the aggressor inputs. We propose a simple procedure to find aggressor alignment for worst-case coupling in all the cases.

Scheduling in the dark

We considered non-clairvoyant multiprocessor scheduling of jobs with arbitrary arrival times and changing execution characteristics. The problem has been studied extensively when either the jobs all arrive at time zero, or when all the jobs are fully parallelizable, or when the scheduler has considerable knowledge about the jobs. This paper considers for the first time this problem without any of these three restrictions although our algorithm is given more resources than the adversary. We provide new upper and lower bound techniques applicable in this more difficult scenario. The results are of both theoretical and practical interest. In our model, a job can arrive at any arbitrary time and its execution characteristics can change through the life of the job from being anywhere from fully parallelizable to completely sequential. We assume that the scheduler has no knowledge about the jobs except for knowing when a job arrives and when it completes. (This is why we say that the scheduler is completely in the dark.) Given all this, we prove that the scheduler algorithm Equi-partition, though simple, performs within a constant factor as well as the optimal scheduler as long as it is given at least twice as many processors. Moreover, we prove that if none of the jobs are “strictly” fully parallelizable, then Equi-partition performs competitively with no extra processors. We also consider other variations: faster processors; fewer preemptions; and a wider range of execution characteristics.

Random trees in queueing systems with deadlines

We survey our research on scheduling aperiodic tasks in real-time systems in order to illustrate the benefits of modelling queueing systems by means of random trees. Relying on a discrete-time single-server queueing system, we investigated deadline meeting properties of several scheduling algorithms employed for servicing probabilistically arriving tasks, characterized by arbitrary arrival and execution time distributions and a constant service time deadline T. Taking a non-queueing theory approach (i.e., without stable-stable assumptions) we found that the probability distribution of the random time sT where such a system operates without violating any task's deadline is approximately exponential with parameter λT = 1μT, with the expectation E[sT] = μT growing exponentially in T. The value μT depends on the particular scheduling algorithm, and its derivation is based on the combinatorial and asymptotic analysis of certain random trees. This paper demonstrates that random trees provide an efficient common framework to deal with different scheduling disciplines and gives an overview of the various combinatorial and asymptotic methods used in the appropriate analysis.

On optimal lateness and tardiness scheduling in real-time systems

We address lateness and tardiness scheduling policies for real-time systems. It is well-known that preemptive Earliest Deadline First (EDF) minimizes the worst lateness and tardiness of a finite set of tasks with known arrival times, service times and deadlines to the finishing time, on a uniprocessor. We extend this result significantly, to include an arbitrary (possibly infinite) number of tasks with arbitrary arrival and service times, and deadlines, and to show thatEDF 1. minimizes the lateness and tardiness of the tasks that are in the system at an arbitrary time. 2. minimizes lateness within a busy interval, for an arbitrary, possibly infinite number of tasks. 3. maximizes the time to the first missed deadline, and 4. minimizes the length of time during which there is at least one missed deadline in the system.

Analysis of two-stage transfer-line production system subject to inter-stage inspection and arbitrary arrival and processing time distributions

The purpose of this paper is to study the transient and steady-state behaviour of a two-stage transfer-line production system subject to attribute type of instantaneous inter-stage inspection. A stochastic model is developed to describe the system and analytical expressions have been obtained for certain measures of performance with arbitrary distributions of arrival and processing time at both the stages of production by using the state-space method. The results obtained by Gopalan and Ramesh [ Int. J. Management Syst. 4(1), 50–66 (1988)] and Gopalan and Anantharaman [ Ind. Engng J. XIX(3), 17–23 (March, 1990)] have been shown to be particular cases.

Modelling the Effect of Transient Faults in Fault Tolerant Computer Systems

The Bounded Set Approach to reliability modelling is extended to the case of transient faults in Fault Tolerant Systems. An arbitrary arrival time distribution is assumed for transient faults rather than a constant rate. The method has been automated and results of several studies are given.

A General Model of a Single-Channel Queue: Discrete and Continuous Time Cases

In Part I, a single-channel service system consisting of a service facility and queue, in which the possible times of arrival of units and the possible service times are discrete, is analyzed. A method of calculating the moments of the total service time of units in the system is developed. This total service time is related to the delay caused by the system. When arrivals at different times are assumed to be independent, the “values” of the resulting Markov process can be calculated. These values lead to information about the transient behavior, autocorrelation function, expected first passage time, and expected extra delay that arises if another unit is inserted into the system. An expression for the geometric transform or moment generating function of the probability distribution of the total service time of units in the system is determined. The results are derived for arbitrary arrival and service time distributions. In Part II, the continuous time analog of the system of Part I is considered and analogous results are determined.