Server Idle Time Research Articles

Structural and queue characterization of a non-Markovian boundary value problem

In this study, we investigate a single server architecture in which the customer service system is not aware of the length of the line that was sent to them. Thus, the system-controlling equations here become what are known as the vacation differential equations. Here, we argue specifically that this vacation is what is causing the oscillations in the performance measurements of the system. The symbolic structure of the differential equation of the non-Markovian queuing problem is introduced in this study. A procedure of maintenance work is included in this model in terms of the vacation stage to support this minimal non-interrupted service system. The findings offer a thorough analysis of the system that enables it to operate more profitably even if it is interrupted by any associated activities. The supplemental variable method solves the queuing problem caused by the aforementioned subsequent outcomes. Estimates are made for the queue size, server idle time, use, and probability generating factors for each operating method. Numerical analysis was performed on specific examples using mathematical software. This strategy is perfectly acceptable because it is regularly employed and makes use of a statistical demarcation method. The graphical representation of this perspective provides precise calculations of the apparent constraints.

An Effective Fault-Tolerance Technique in Web Services: An Approach Based on Hybrid Optimization Algorithm of PSO and Cuckoo Search

Software rejuvenation is an effective technique to counteract software aging in continuously-running application such as web service based systems. In client-server applications, where the server is intended to run perpetually, rejuvenation of the server process periodically during the server idle times increases the availability of that service. In these systems, web services are allocated based on the user’s requirements and server’s facilities. Since the selection of a service among candidates while maintaining the optimal quality of service is an Non-Deterministic Polynomial (NP)-hard problem, Meta-heuristics seems to be suitable. In this paper, we proposed dynamic software rejuvenation as a proactive fault-tolerance technique based on a combination of Cuckoo Search (CS) and Particle Swarm Optimization (PSO) algorithms called Computer Program Deviation Request (CPDR). Simulation results on Web Site Dream (WS-DREAM) dataset revealed that our strategy can decrease the failure rate of web services on average 38.6 percent in comparison with Genetic Algorithm (GA), Decision-Tree (DT) and Whale Optimization Algorithm (WOA) strategies.

Queuing system in VLSI physical design

The rapid development and communication of PCs requires a steadily increasing number of chips, which must be very small, energy-saving and more elitist. The physical structure (PD) is one of the basic structure squares used in large integrated circuits (VLSIs) of mixed code circuits. The process of transferring a dismantled network at the door level to a physically viable organization and finally to equipment is called Physical Design (PD). Physical Design (PD) is an event characterized by network search and associated frameworks by routing them through a metal layer stack to meet scheduling regulations such as design, performance, and region (PPA). It is not possible to physically carry out all the progress of the planning process, which is time consuming and error prone. The process performed by this design is examined by queuing theory. The queuing problem that occurs with the above structural steps is shown in the schematic and solved using the supplementary variable method. The queue size, server idle time, utilization, and probabilistic generating functions of various means of execution are derived. Special cases were discussed in numerical analysis. This model is very legal due to its practical application and mathematical demarcation method. The graphical overview provides accurate measurements of the limits attempted in this overview.

Efficient improved ant colony optimisation algorithm for dynamic software rejuvenation in web services

Software rejuvenation is an effective technique to counteract software ageing in continuously-running applications such as web-service-based systems. In a client-server application, where the server is intended to run perpetually, rejuvenation of the server process periodically during the server idle times increases the availability of that service. In these systems, web services are allocated based on the receiver's requirements and server's facilities. Since the selection of a server among candidates while maintaining the optimal quality of service is an NP-hard problem, meta-heuristics seems to be suitable. In this study, the proposed dynamic software rejuvenation as a proactive fault-tolerance technique based on a combination of ant colony optimisation (ACO) and gravitational emulation local search (GELS) so as to determine the optimal times when rejuvenation can be performed and failure rate can be minimised. The newly proposed method combined the public search capabilities of ACO with local search of GELS algorithm in an effort to create a stable algorithm, which can make reaching the global optimum largely possible in the proposed work. The simulation results revealed that the proposed strategy can decrease the failure rate of web services averagely by 28% in comparison with genetic algorithm and decision-tree strategies.

Non-indexability of the stochastic appointment scheduling problem

Consider a set of jobs with independent random service times to be scheduled on a single machine. The jobs can be surgeries in an operating room, patients’ appointments in outpatient clinics, etc. The challenge is to determine the optimal sequence and appointment times of jobs to minimize some function of the server idle time and service start-time delay. We introduce a generalized objective function of delay and idle time, and consider l1-type and l2-type cost functions as special cases of interest. Determining an index-based policy for the optimal sequence in which to schedule jobs has been an open problem for many years. For example, it was conjectured that ‘least variance first’ (LVF) policy is optimal for the l1-type objective. This is known to be true for the case of two jobs with specific distributions. A key result in this paper is that the optimal sequencing problem is non-indexable, i.e., neither the variance, nor any other such index can be used to determine the optimal sequence in which to schedule jobs for l1 and l2-type objectives. We then show that given a sequence in which to schedule the jobs, sample average approximation yields a solution which is statistically consistent.

Variant impatient behavior of a Markovian queue with balking reserved idle time and working vacation

The customers’ impatience and its effect plays a major role in the economy of a country. It directly affects the sales of products and profit of a trading company. So, it is very important to study various impatient behaviors of customers and to analyze different strategies to hold such impatient customers. This situation is modeled mathematically in this research work along with working vacation and reserved idle time of server, balking and re-service of customers. This paper studies the transient analysis of anM/M/1 queueing model with variant impatient behavior, balking, re-service, reserved idle time and working vacation. Whenever the system becomes empty, the server resumes working vacation. When he is coming back from the working vacation and finding the empty system, he stays idle for a fixed time period known as reserved idle time and waits for an arrival. If an arrival occurs before the completion of reserved idle time, the server starts a busy period. Otherwise, he resumes another working vacation after the completion of reserved idle time. During working vacation, the arriving customers may either join or balk the queue. The customers waiting in the queue for service, during working vacation period, become impatient. But, the customer who is receiving the service in the slow service rate, does not become impatient. After each service, the customer may demand for immediate re-service. The transient system size probabilities for the proposed model are derived using generating function and continued fraction. The time-dependent mean and variance of system size are also obtained. Finally, numerical illustrations are provided to visualize the impact of various system parameters.

Evaluation of appointment scheduling rules: A multi-performance measurement approach

Appointment scheduling rules are used to determine when a customer is to receive service during a service session. In general, appointment scheduling rules do not consider the sequencing of individual customers, but provide simple guidelines on how to assign appointment times to a set of (arriving) customers. Many appointment scheduling rules exist and are being used in practice (e.g., in healthcare and legal services). Which appointment scheduling rule is best, however, is still an open question. In order to answer this question, we develop an analytical model that allows to assess the performance (in terms of customer waiting time, server idle time, and server overtime) of appointment scheduling rules in a wide variety of settings. More specifically, the model takes into account: (1) customer unpunctuality, (2) no-shows, (3) service interruptions, and (4) delay in session start time. In addition, we allow the use of general distributions to capture system processes. We adopt an efficient algorithm (with respect to computational and memory requirements) to assess the performance of 314 scheduling rules and use data envelopment analysis to identify the rules that have good, robust performance in a wide variety of settings.

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.

Comparison of three vacation policies in discrete time inventory system with postponed demands

In this paper, we consider a single server discrete time inventory system with postponed demands and server vacation. Arrival process follows DMAP and ordering policy follows policy with geometrically distributed lead time. Due to depletion of inventory in the stock to zero, server may avail vacation immediately or after some random time. Here, we proposed three different vacation policies, namely modified multiple vacation (random idle time before each vacation), single (only one vacation) and multiple (one after another vacation). The demand who arrives during the stock-out period or server vacation period enters the pool of infinite size. These pooled demands are selected one-by-one according to a rule. The vacation time, the server idle time and the inter-selection time follow independent DPH distribution. The joint probability distribution of the number of demands in the pool, the server status, the on-hand inventory level is obtained in the steady-state case. We derived the total expected cost function in the steady-state case for each vacation model. We present some numerical examples and try to justify the best vacation policy for different parameter rates. Also, we analyse the impact of system costs on the total optimal cost of modified multiple vacation policy.

Improving efficiency in service systems by performing and storing “preliminary services”

We propose a novel approach to improve efficiency in service systems. The idea is to utilize the server's idle time to perform and store “preliminary services” for customers who will arrive in the future. Such a model is relevant to settings in which service consists of multiple consecutive tasks, some of which are generic and needed by all customers (and thus can be performed even in their absence), while other require the customer's presence. To show the model's benefits, we formulate a two-dimensional single-server queueing-inventory system for which we derive closed-form expressions for the system's steady-state probabilities, as well as for its performance measures. Assuming linear costs for customers waiting in line and for stored preliminary services, a cost analysis determines the optimal maximal number of stored preliminary services in the system. Numerical examples illustrated with graphs demonstrate the advantages of our approach, in terms of cost savings, as compared with the classical M/M/1 model.

Heavy-traffic limits for server idle times with customary server-assignment rules

Sun and Whitt (2017) developed a class of server-assignment rules that can help create effective breaks for servers from naturally available idleness. They found that the standard longest-idle-server-first rule and the alternative random routing generate breaks too infrequently. This paper provides theoretical justifications for these empirical findings by establishing the many-server heavy-traffic limits for server idle times with customary assignment rules. We gain insights into the server idle–busy activity patterns resulting from the server-assignment schemes in the system.

A queueing system with decomposed service and inventoried preliminary services

• Producing preliminary services in the absence of customers. • Formulating a quasi birth-and-death process and using matrix geometric analysis. • Deriving the process steady-state probabilities and system’s performance measures. • Discovering that the entries of the rate matrix are related to Catalan numbers. • Deriving explicitly the PDF of a customer’s sojourn time. We study a single-server queue in which the service consists of two independent stages. The first stage is generic and can be performed even in the absence of customers, whereas the second requires the customer to be present. When the system is empty of customers, the server produces an inventory of first-stage (‘preliminary’) services (denoted PSs), which is used to reduce customers’ overall sojourn times. We formulate and analyze the queueing-inventory system and derive its steady-state probabilities by using the matrix geometric method, which is based on calculating the so called rate matrix R . It is shown that the system's stability is not affected by the production rate of PSs, and that there are cases in which utilizing the server's idle time to produce PSs actually increases the fraction of time during which the server is dormant. A significant contribution is the derivation of an explicit expression of R , whose entries are written in terms of Catalan numbers. This type of result is rare in the literature and enables large-scale problems to be solved with low computational effort. Furthermore, by utilizing Laplace–Stieltjes transform and its inverse, we obtain the distribution function of customers’ sojourn time. Finally, based on the probabilistic study, we carry out an economic analysis using a practical example from the fast food industry.

Routing and Staffing When Servers Are Strategic

Traditionally, research focusing on the design of routing and staffing policies for service systems has modeled servers as having fixed (possibly heterogeneous) service rates. However, service systems are generally staffed by people. Furthermore, people respond to workload incentives; that is, how hard a person works can depend both on how much work there is and how the work is divided between the people responsible for it. In a service system, the routing and staffing policies control such workload incentives; and so the rate servers work will be impacted by the system’s routing and staffing policies. This observation has consequences when modeling service system performance, and our objective in this paper is to investigate those consequences. We do this in the context of the M/M/N queue, which is the canonical model for large service systems. First, we present a model for “strategic” servers that choose their service rate to maximize a trade-off between an “effort cost,” which captures the idea that servers exert more effort when working at a faster rate, and a “value of idleness,” which assumes that servers value having idle time. Next, we characterize the symmetric Nash equilibrium service rate under any routing policy that routes based on the server idle time (such as the longest idle server first policy). We find that the system must operate in a quality-driven regime, in which servers have idle time, for an equilibrium to exist. The implication is that to have an equilibrium solution the staffing must have a first-order term that strictly exceeds that of the common square-root staffing policy. Then, within the class of policies that admit an equilibrium, we (asymptotically) solve the problem of minimizing the total cost, when there are linear staffing costs and linear waiting costs. Finally, we end by exploring the question of whether routing policies that are based on the service rate, instead of the server idle time, can improve system performance.

SIMULATION MODELS FOR CEMENT LOADING PROCESS

Reduction of waiting and throughput times of cement trucks in cement-loading processes generally requires additional input resources, such as cement-loading machines and operators. However, a superfluous number of input resources can increase idle time. On the other hand, minimizing input server resources can significantly save costs for cement plants, but would result in excessive waiting time and throughput time of trucks, limiting the number of trips that trucks could travel to transport cement. To maximize the utilization of cement trucks and input resources, a trade-off between truck waiting time and server idle time is necessary. This study developed a simulation model maximizing the utilization factor of truck waiting time and machine idle time. By using EZStrobe software, the current operations of the cement-loading process were simulated based on data obtained between August 2012 and June 2013 at Asia Cement Plant, Thailand. The results show that a new design of operations with alternate layout, which operates by using four regular cement-loading channels with two extra channels during the 8-hour peak duration, is recommended for the cement-loading process to optimize performance, since they reduce truck waiting time, throughput time, and queue length, with the lowest machine idle time possible.

Sequencing Appointments for Service Systems Using Inventory Approximations

Managing appointments for service systems with random job durations is a challenging task. We consider a class of appointment planning problems that involve two sets of decisions: job sequencing, i.e., determining the order in which a list of jobs should be performed by the server, and appointment scheduling, i.e., planning the starting times for jobs. These decisions are interconnected because their joint goal is to minimize the expected server idle time and job late-start penalty costs incurred because of randomness in job durations. In this paper, we design new heuristics for sequencing appointments. The idea behind the development of these heuristics is the structural connection between such appointment scheduling problems and stochastic inventory control in serial supply chains. In particular, the decision of determining time allowances as buffers against random job durations is analogous to that of selecting inventory levels as buffers to accommodate random demand in a supply chain; having excess buffers in appointment scheduling and supply chain settings incurs idle time and excess inventory holding costs, respectively, and having inadequate buffers leads to delays of subsequent jobs and backorders, respectively. Recognizing this connection, we propose tractable approximations for the job sequencing problem, obtain several insights, and further develop a very simple sequencing rule of ordering jobs by duration variance to late-start penalty cost ratio. Computational results show that our proposed heuristics produce close-to-optimal job sequences with significantly reduced computation times compared with those produced using an exact mixed-integer stochastic programming formulation based on the sample-average approximation approach.

Sequencing Appointments for Service Systems Using Inventory Approximations

Managing appointments for service systems with random job durations is a challenging task. We consider a class of appointment planning problems that involve two sets of decisions: job sequencing, i.e., determining the order in which a list of jobs should be performed by the server, and appointment scheduling, i.e., planning the starting times for jobs. These decisions are interconnected because their joint goal is to minimize the expected server idle time and job late-start penalty costs incurred due to randomness in job durations. In this paper, we design new heuristics for sequencing appointments. The idea behind the development of these heuristics is the structural connection between such appointment scheduling problems and stochastic inventory control in serial supply chains. In particular, the decision of determining time allowances as buffers against random job durations is analogous to that of selecting inventory levels as buffers to accommodate random demand in a supply chain; having excess buffers in appointment scheduling and supply chain settings incurs idle time and excess inventory holding costs, respectively, and having inadequate buffers leads to delays of subsequent jobs and back orders, respectively. Recognizing this connection, we propose tractable approximations for the job sequencing problem, obtain several insights, and further develop a very simple sequencing rule of ordering jobs by duration variance to late-start penalty cost ratio. Computational results show that our proposed heuristics produce close-to-optimal job sequences with significantly-reduced computation times compared with those produced using an exact mixed integer stochastic programming formulation based on the sample-average approximation approach.The appendices for this paper are available at the following URL: http://ssrn.com/abstract=2352901

Evaluation of Appointment Scheduling Rules: A Multi-Performance Measures Approach

Appointment scheduling rules are used to determine when a customer is to receive service. Many appointment scheduling rules exist and are being used in practice (e.g., in healthcare and legal services). Which appointment scheduling rule is best, however, is still an open question. In order to answer this question, we develop an analytical model that allows to assess the performance (in terms of customer waiting time, server idle time and server overtime) of appointment scheduling rules in a wide variety of settings. More specifically, the model takes into account: (1) customer unpunctuality, (2) no-shows, (3) service interruptions and (4) delay of the service process. In addition, we allow the use of general distributions to capture system processes. We adopt an efficient algorithm (with respect to computational and memory requirements) to assess the performance of 314 scheduling rules and use data envelopment analysis to compare results.

Delay Distributions in Appointment Systems with Generally and Non-Identically Distributed Service Times and No-Shows

We derive the probability distribution of each patient's wait time and doctor's idle time and overtime in single-server systems where healthcare providers respond to appointment-driven arrivals with generally and non-identically distributed service times. Patient no-show probabilities and appointment intervals are also non-identical. The formulation is due to a convolution-based busy period analysis that can be implemented via numerical integration methods. A special case yields the distribution of customer wait times and server idle times in transient-phase D/M/1 queues for appointments at fixed-intervals, where analytical distribution functions facilitate a mathematical proof that delays are unfair to patients. We demonstrate more generally that appointment system assessment of delay tail probabilities (rather than expectations) considers the non-linear disutility for delays, and indeed reverses conclusions made in prior analysis.

두 단계 서비스 시스템에서 교차예약정책의 평가

The appointment system is widely used to facilitate customer access to service in many industries including healthcare and others. Because of its importance, much research has investigated how to build an effective appointment policy under various environments. However, most research has considered a single-server service system. The objective of this work is to evaluate several appointment policies in a two-stage service system in which multiple servers are available and build separate appointments at the second-stage. In such a system, we propose and evaluate the staggering appointment policy. Simulation experiments indicate that the proposed staggering appointment policy outperforms other traditional appointment policies in terms of customer waiting time, server idle time, and the number of customers who are later to scheduled appointments.

Convergence of a queueing system in heavy traffic with general patience-time distributions

We analyze a sequence of single-server queueing systems with impatient customers in heavy traffic. Our state process is the offered waiting time, and the customer arrival process has a state dependent intensity. Service times and customer patient-times are independent; i.i.d. with general distributions subject to mild constraints. We establish the heavy traffic approximation for the scaled offered waiting time process and obtain a diffusion process as the heavy traffic limit. The drift coefficient of this limiting diffusion is influenced by the sequence of patience-time distributions in a non-linear fashion. We also establish an asymptotic relationship between the scaled version of offered waiting time and queue-length. As a consequence, we obtain the heavy traffic limit of the scaled queue-length. We introduce an infinite-horizon discounted cost functional whose running cost depends on the offered waiting time and server idle time processes. Under mild assumptions, we show that the expected value of this cost functional for the n -th system converges to that of the limiting diffusion process as n tends to infinity.