Heterogeneous Arrivals Research Articles

Multi-objective optimization of production system with staggered production

In the manufacturing industry, timely order fulfilment from diverse customers is important for operational profitability, given the constraints of limited production capacity. This paper proposes a novel queueing system for a production system, in which order processing times are categorised as regular or rush based on customer preference. The proposed queueing system employs variable service rates and service strategies in conjunction with staggered production to deal with heterogeneous arrivals. We compute the steady-state probability distribution and develop system performance indicators. The lower and upper bounds of the expected sojourn time for rush and regular orders are derived. Numerical results show that an appropriate switching policy can reduce rush orders by approximately 35% while regular orders increase by less than 10%, demonstrating significant improvement in order fulfilment management. We formulate a multi-objective optimisation problem and implement the NSGA-II algorithm to obtain Pareto optimal solutions. Finally, three regression models are proposed to determine the minimum cost and the associated optimal service rates, given the maximum acceptable value of the expected number of rush orders. The established models can explain at least 80% of the dataset of the optimal solutions and thus our numerical findings provide useful guidance for decision-makers and production managers.

Transient Numerical Analysis for Markovian Heterogeneous Arrivals Queue With Working Vacation, Two-Phase Service and Impatient Customers

Transient Numerical Analysis for Markovian Heterogeneous Arrivals Queue With Working Vacation, Two-Phase Service and Impatient Customers

Multi-server Markovian heterogeneous arrivals queue with two kinds of working vacations and impatient customers

This paper deals with multi-server queueing system with two kinds of Working Vacations (WVs) and impatient customers. A random timer is started whenever a customer comes into the system. The customer may abandon the system if the service is not completed before the impatience timer expires. Each time after serving all the customers, the system becomes empty and then the server begins 1st kind of vacation. On returning from 1st kind of WV, the server begins 2nd kind of WV whenever a system has no customers. When the server comes back from either 1st kind or 2nd kind of WV, if there is at least one customer in the system, the server switches to busy period. The steady state probabilities have been derived using the Probability Generating Functions (PGFs) method. Various measures of performance are presented and numerical illustrations are also provided.

The impact of heterogeneous arrival and departure rates of flights on runway configuration optimization

ABSTRACT The rapid growth of the airline industry has caused an enormous demand in the context of air transport and air traffic congestion in several hub airports. In order to alleviate this situation and resolve the imbalance between the arrival and departure rate, efficient runway usage in airport capacity management is an immediate and feasible solution as compared to airport expansion and runway construction. Air Traffic Control (ATC) operators could optimize their runway capacity by operating dynamic runway configuration in switch-mode runways based on the air and airport traffic conditions. A semi-mixed mode runway is considered in this paper, wherein some runways are configured for either landing or take-off operations, while others are operated in switch mode. The demand for arrival and departure is subject to the passenger's demand, flight availability, and timings, preferred flight schedule, and frequency of flight schedule service, and usually vary in different hours (peak and nonpeak hours). Given this feature, ATC can reconfigure the runway mode responding to the current demand for arrival and departure and further seize the runway capacity via a systematic approach. Under the semi-mixed mode situation, formulating the coordination of dynamic runway configuration planning and the Aircraft Sequencing and Scheduling Problem is proposed. The air traffic pattern in Hong Kong International Airport (HKIA) is used as a test case to evaluate the performance of this proposed model. Based on the test results, it was found that this dynamic runway configuration planning and semi-mixed runway design can utilize runway capacity more efficiently. In the numerical study, the dynamic runway configuration planning achieved 71.6%% and 37.08% reduction of flight tardiness than the two segregated runway systems (two landings and one take-off runways and one landing and two take-off runways) in HKIA.

A Random Compensation Scheme for 5G Slicing Under Statistical Delay-QoS Constraints

For the communication scenarios of heterogeneous arrivals in the fifth generation cellular networks, slicing is believed to be an effective way to provide quality-of-service (QoS) provisioning. However, the reports on an effective segmentation of resources for random and bursty arrival are rare. Relying on the bandwidth estimation and service design, we give a simple but effective scheme for the slicing of bandwidths named two-hole leaky bucket random service mechanism. The service in our scheme comprises two parts, the specific basic service and shared random compensation service. Accordingly, the mechanism of resource allocation is just like leaky bucket with two holes, one of which has a random leak rate. To guarantee the statistical QoS of heterogeneous traffic flows, effective bandwidth/capacity theory is introduced into the slicing scheme. By establishing function equations, we deduce the compensation probability of each slice, which is taken as the slicing adjustment factor. Simulation results prove that the random compensation scheme can satisfy the statistical QoS requirements of heterogeneous traffic flows. Although the scheme is proved to be effective against two slices, the proposed model is applicable to general multiple heterogeneous arrivals.

Router Buffer Behavior Analysis for Aggregate Traffic Based on Martingale Method

The buffer behavior of routers has an important influence on the quality of service of network services. Exploring theory and methods to analyze the characteristics of the buffer is an interesting job, especially when aggregate traffic is transmitted. This letter investigates the buffer behavior of a single server queuing system with multiple arrival flows, which models the operations of a router. A martingale analytical framework is proposed, which could evaluate buffer performance for aggregate traffic arrivals with different distributions. We use the processes of arrival and service to construct martingales, and analyze the queuing system with heterogeneous arrivals in martingale domain. Applying the stopping time theory of martingale, the transient performance of queue buffer is presented. The probability of buffer overflow and the expectation of buffer stopping time are derived together in this model. The simulations are given to validate the analytical results. This investigation provides a valuable reference for router buffer design.

Technical Note—Intertemporal Price Discrimination via Reference Price Effects

We consider the dynamic pricing problem a monopolistic seller faces when customers arrive in heterogeneous time periods and their purchase decisions are affected by reference prices formed from their past observations of prices. We illustrate that a new form of price discrimination opportunity exists in such situations, where the seller’s optimal pricing strategy is a cyclic one, even when the customers are loss-neutral and their demand functions are identical. This result differs from those of prior studies where the optimal price paths are shown to be asymptotically constant and thus is unique due to the interaction between the heterogeneous arrivals and the reference price effects. We also provide the cycle length of the optimal pricing policy when the demand function is linear and when customers are loss-neutral. In this era when customer information is easier accessible, our results suggest the sellers consider this new dimension of price discrimination in conjunction with the old ones, to take advantage of the full power of customer data.

Intertemporal Price Discrimination via Reference Price Effects

We consider the dynamic pricing problem a monopolistic seller faces when customers arrive in heterogeneous time periods and their purchase decisions are affected by reference prices formed from their past purchase experiences. We illustrate that a new form of price discrimination opportunity exists in such situations, where the seller’s optimal pricing strategy is a cyclic one, even when the customers are loss-neutral and their demand functions are identical. This result differs from those in prior studies where the optimal price paths are shown to be asymptotically constant when customer arrival times are homogeneous or when there are no reference price effects, thus is unique due to the interaction between the heterogeneous arrivals and the reference price effects. We also provide the length of the cycle when the demand function is linear. In this era where customer information becomes easier accessible, our results suggest the seller consider this new dimension of price discrimination in conjunction with the old ones, in order to take advantage of the full power of customer data.

Analysis of discrete-time buffers with heterogeneous session-based arrivals and general session lengths

In this paper we study the effect of session-based arrival streams on the behavior of a discrete-time queueing system with infinite storage capacity and a single output line. These session-based arrival streams are a new and realistic approach for modelling traffic generated by users in a telecommunication network. Users from an infinite population can start and end sessions during which they are active and send packets to the queueing system. Each active user generates a random, yet strictly positive number of packets per time slot. There are T different sessions types, each characterized by their own general session-length, session-incidence and bandwidth distribution.The corresponding discrete-time queueing model is analyzed by a generating-functions approach with infinite-dimensional state description. We derive the steady-state probability generating functions of the buffer content and the packet delay. From these, we obtain the mean buffer content as well as the mean packet delay and even the mean session delay. Finally, some numerical examples illustrate the influence of various parameters on the buffer behavior.

Delay-Optimal User Scheduling and Inter-Cell Interference Management in Cellular Network via Distributive Stochastic Learning

In this paper, we propose a distributive queue-aware intra-cell user scheduling and inter-cell interference (ICI) management control design for a delay-optimal celluar downlink system with M base stations (BSs), and K users in each cell. Each BS has K downlink queues for K users respectively with heterogeneous arrivals and delay requirements. The ICI management control is adaptive to joint queue state information (QSI) over a slow time scale, while the user scheduling control is adaptive to both the joint QSI and the joint channel state information (CSI) over a faster time scale. We show that the problem can be modeled as an infinite horizon average cost Partially Observed Markov Decision Problem (POMDP), which is NP-hard in general. By exploiting the special structure of the problem, we shall derive an equivalent Bellman equation to solve the POMDP problem. To address the distributive requirement and the issue of dimensionality and computation complexity, we derive a distributive online stochastic learning algorithm, which only requires local QSI and local CSI at each of the M BSs. We show that the proposed learning algorithm converges almost-surely (with probability 1) and has significant gain compared with various baselines. The proposed solution only has linear complexity order O(MK).

Heterogeneous information flows and intra-day volatility dynamics: evidence from the UK FTSE-100 stock index futures market

Recent research has suggested that intra-day volatility may possess a component structure due to heterogeneous information arrivals. This paper reports evidence for the existence of such components in FTSE-100 stock index futures returns data. Preliminary GARCH model estimates support previous evidence for other markets indicating the breakdown of theoretical GARCH temporal aggregation properties over the intra-day period. However, the fractional integration properties of absolute and squared returns, and FIGARCH conditional volatility model estimates, lend strong support to the contention that volatility dynamics results from multiple sources given the invariance of the fractional difference parameter estimates to the degree of intra-day data temporal aggregation.

Market trader heterogeneity and high frequency volatility dynamics: further evidence from intra-day FTSE-100 futures data

Recent research has suggested that intra-day volatility may possess a component structure, though views differ as to whether this is the consequence of heterogeneous information arrival or the actions of heterogeneous market agents. Estimation results for a HARCH conditional variance model which defines volatility components over differing time horizons provides confirmatory evidence of heterogeneous market components and support for the interpretation of such components as resulting from the presence of different trader types, in which context the impact of high-frequency speculation and noise-trading are particularly apparent.

Analysis of a Discrete-Time Queueing System with a Single Server and Heterogeneous Markovian Arrivals

We consider a discrete-time queueing system with a single deterministic server, heterogeneous Markovian arrivals and finite capacity. Most existing techniques model the queueing system using a direct bivariate Markov chain which requires a state space that grows rapidly as the number of customer types increases. In this paper, we define renewal cycles in terms of the input process and model the system occupancy level on each renewal cycle using a one-dimensional Markov chain. We derive the exact joint steady-state probability distribution of both states of input and system occupancy with a considerably reduced state space, which leads to the efficient calculation of overall/individual performance measures such as loss probability and average delay.

A steady-state analysis of optimal threshold policy with heterogeneous arrivals to the M/G/1 queue

An M/G/1 queue with general server setup time under a control policy is studied. We consider the case when the arrival rate varies according to the server's status: idle, setup and busy states. For this model, the optimal N-value from which the server starts his setup is found by minimizing the total operation cost of the system.

Admission Policies in Loss Queueing Models with Heterogeneous Arrivals

In this paper we consider a loss system where the arrivals can be classified into different groups according to their arrival rate and expected service time. While the standard admission policy consists of rejecting only those customers who arrive when all servers are busy, we address the problem of finding the optimal static admission policy (with respect to a given reward structure) when customers can be discriminated according to the group they belong to, thus customers of some groups might be automatically rejected (even if some servers remain idle) in order to enhance the global efficiency of the system. The optimality of a cμ-rule is shown, from which finite-time algorithms for the one- and two-server cases are derived.

Bandwidth assignment paradigms for broadband integrated voice/data networks

Broadband Integrated Services Digital Networks (BISDNS)/Asynchronous Transfer Mode (ATM) are expected to support diverse applications demanding different bandwidth and Quality of Services (QoSs). Particularly for integrated voice and data networks, voice traffic results in call losses and data traffic suffers from longer delays should networks have insufficient bandwidth. The main goal of the paper is to analytically determine optimal bandwidth allocated to voice and data by means of a queueing model with heterogeneous arrivals and multiple designated channels. The accuracy of analytical results is confirmed by simulation results. On the basis of the analysis, the paper proposes a bandwidth assignment paradigm for the assignment of network bandwidth to voice and data in an effort to guarantee minimal data delay and voice call blocking probability. The run time complexity of the bandwidth assignment computation and paradigm construction is shown to be polynomial bounded. Consequently, the resulting bandwidth assignment assures QoSs in terms of data delay and voice call blocking probability under various network loads.

Performance Analysis Of Earliest-Due-Date Scheduling Discipline For Atm Switches

Asynchronous transfer mode (ATM) networks are expected to support a diverse mix of traffic sources with different quality-of-service (QOS) requirements. To providing satisfactory QOS to ali network users, ATM networks are often required to prioritize users' traffic based on their service requirements. This paper initially examines several existing scheduling disciplines that offer delay guarantees for multiple service classes. Among them, the earliest-due-date (EDD) discipline has been regarded as one of the most promising scheduling disciplines. The EDD discipline schedules the departure of a cell belonging to a call baaed on the delay priority assigned for that call during the call set-up. Considering 71 delay-based service classes associated with n urgency numbers D0 to Dn-1 (D0 ≤ D1 ≤ . ≤ Dn-1) respectively, EDD allows a class-i cell to precode any class-j (j > i) cell arriving not prior to (Dj - Di)- slot time. The main goal of the paper is to determine the urgency numbers (Di's), based on a decent queueing analysis, in an attempt to offer satisfactory delay guarantees for higher priority calls while incurring only minima] delay degradation for lower priority calls. In the analysis, we derive the system-time distributions assuming two servies classes, based on a discrete-time, single-server queueing model with heterogeneous arrivals including renewal and nonrenewal arrival processes. On the basis of the analysis, the urgency numbers (Dis) can be dynamically and effectively adj usted to provide a ninety-nine percentile delay guarantee for high priority calls under various traffic loads. Finally, we demonstrate the accuracy of the analysis via simulation results.

Neural-network-based call admission control in ATM networks with heterogeneous arrivals

Call Admission Control (CAC) has been accepted as a potential solution for supporting diverse, heterogeneous traffic sources demanding different Quality of Services (QOSs) in ATM networks. Also, CAC is required to consume a minimum of time and space to make call acceptance decisions. In this paper, we present an efficient neutral-network-based CAC (NNCAC) mechanism for ATM networks with heterogeneous arrivals. All heterogeneous traffic calls are initially categorized into various classes. Based on the number of calls in each class, NNCAC efficiently and accurately estimates the cell delay and cell loss ratio of each class in real time by means of a pre-trained neutral network. According to our decent study which exhibits the superiority of the employment of analysis-based training data over simulation-based data, we particularly construct the training data from a heterogeneous-arrival dual-class queueing model M [ N 1] + I [ N 2] / D/1/ K, where M and I represent the Bernoulli and interrupted Bernoulli processes, and N 1 and N 2 represent the corresponding numbers of calls, respectively. Analytic results of the queueing model are confirmed by simulation results. Finally, we demonstrate the profound agreement of our neural-network-based estimated results with analytic results, justifying the viability of our NNCAC mechanism.

Transient analysis of queues with heterogeneous arrivals

In this paper we consider a discrete time queueing model where the time axis is divided into time slots of unit length. The model satisfies the following assumptions: (i) an event is either an arrival of typei of batch sizebi, i=1,...,r with probabilityαi or is a depature of a single customer with probabilityγ or zero depending on whether the queue is busy or empty; (ii) no more than one event can occur in a slot, therefore the probability that neither an arrival nor a departure occurs in a slot is 1−γ−⌆iαi or 1−⌆iαi according as the queue is busy or empty; (iii) events in different slots are independent. Using a lattice path representation in higher dimensional space we will derive the time dependent joint distribution of the number of arrivals of various types and the number of completed services. The distribution for the corresponding continuous time model is found by using weak convergence.

A nonpreemptive priority multiserver queueing system with general bulk service and heterogeneous arrivals

In this paper a multiserver nonpreemptive priority queueing system consisting of two types of customer units with Poisson arrival and exponential service time distribution is analysed. The lower priority units are served in batches according to a general bulk service rule. The higher priority units have nonpreemptive priority over lower priority units. The higher priority units are served singly. The steady state probability vectors of the number of customers in the queue are obtained using the modified matrix-geometric method. The stability condition and mean queue length of customers are obtained. Numerical results are also presented.