In this paper, we have described an analytical model for performance evaluation of a highly virtualized cloud com- puting center under Poisson batch arrivals with generally distributed task sizes and generally distributed task service times, with additional correction for performance deteri- oration under heavy workload. The model is based on a two-stage approximation technique where the original non- Markovian process is first modeled with an embedded semi- Markov process, which is then modeled by an approximate embedded Markov process but only at the time instants of super-task arrivals. This technique provides accurate computation of important performance indicators such as the mean number of tasks in the system, queue length, mean response and waitingtime, blocking probability and the probability of immediate service.
On the other hand steady-state results are typically much easier to obtain and can provide results that, whilst often biased, are nevertheless sufficiently accurate for decision-making. One popular method of using steady- state results is as a Simple Stationary Approximation (SSA), in which a simple average arrival rate is used to derive steady-state results as an approximation for the overall behaviour of the system. This approach can be valuable if used carefully, but it can also lead to serious errors. For example Eick, Massey & Whitt  show that using the steady-state result for the M/G/∞ queue to approximate the M(t)/G/∞ queue with sinusoidal arrival rates provided the correct overall mean number in the system. However it obviously misses the time dependent and hence distributional form of number in the system. For systems with finite numbers of servers, particularly when the servers are often all busy, the non-linear relationship between congestion and traffic intensity implies that the overall congestion in the system for a M(t)/G/c model will generally be underestimated by a M/G/c approximation. For example Green, Kolesar & Svoronos  found that using the steady-state M/M/c model to approximate an M(t)/M/c system where actual arrival rate was sinusoidal and varied by only 10% about its average resulted in significant underestimations.
The MIP model schedules OC and OR blocks over the available doctor capacity while in- corporating future capacity and demand. We define S as set of doctors. Set T is the set of weeks in the planning horizon. Furthermore, we consider set I as the set of queues for each doctor s , A as the set of stations and N as set of time periods a patient is waiting. We define both the routing matrix and the delay matrix, as the Cartesian product of |I| · |I| for each doctor s . This implies that internal transitions between doctors are not allowed. The routing matrix is filled with the transition rates that result from Phase 1. We fill the delay matrix with the deterministic delays as calculated based on historical data as we explain in Appendix C.2. The weight-factor matrix consist of the Cartesian product of |N | · |I| for all doctors s . As a starting point, we choose to let the weight-factors increase linearly with the form Ax + b where A = 2 and b = − 1. Initially, we do not distinguish between queues. The weekly doctor capacity, denoted by integer parameter a s,t , should be divided over sta-
Quality information on service delay (QDI) refers to service provider’s communication of timely and appropriate information about service delay to customers waiting for service, either in the pre-service encounter or service-encounter situations. Service providers could also provide customers with quality information on an unplanned and planned delay for service delivery (Antonides et al., 2002; Lee et al., 2012; Lin et al., 2015). Where service delivery is likely to be delayed as a result of technical operational factors beyond the control of bank service provider, especially within the short-term, there is the need to communicate such delay information to customers well in advance (Bae and Kim, 2014). Such advanced information on likely service delays enables bank customers to make their own adjustment to overcome the effect of the delay in service. It also gives customers an impression that service providers are in control of the service delivery process, strengthening service providers’ ability to management the service delivery process and provide assurance and security to customer for service delivery, while enforcing customer confidence in service provider’s ability to deliver in service co-creation (Gohary et al., 2016; Jaakkola and Alexander, 2014; Vargo and Lusch, 2014). However, Kumar and Krishnamurthy (2008) found that service-time uncertainty in anticipated congestion has a critically negative impact on customers’ waiting-time decisions. Thus, where service providers can provide quality delay information it could lead to waitingtime satisfaction in customers. Therefore, we hypothesise that:
Not knowing when a waiting situation is going to end can cause a lot of uncertainty (Branaghan & Sanchez, 2008 & 2009; Han et al., 2015). In the setting of waiting for a delayed nationwide train uncertainty plays a very important role, because in that context of a rather long journey people have and want to fulfill certain needs while waiting such as buying food or coffee, and going to the toilet for instance. But the problem in those waiting situations is that despite the announcements, travelers are still often unsure about the exact remaining waitingtime and thus would not dare to leave the platform to fulfill such a need being afraid to eventually miss their train. This uncertainty thus impacts travelers’ psychological well- being, which can further affect the overall satisfaction with the service (Pruyn & Smidts, 1998). Hence, it is important to try to reduce uncertainty.
Waiting lists for elective surgery (WLES) are problematic for public healthcare systems, because patients often expe- rience long waiting times with a negative impact on health and quality of life [1-4]. WLES represent dynamical sets where behavior is unpredictable and policy interventions are difficult to assess . Since the 1960s, research has shifted in the field of prioritization with the aim of ensur- ing prompt access for patients most in need. Although sev- eral models were proposed , they were based on different principles without great international agree- ment. Different tools were developed for elective surgery either based on implicit semi quantitative or explicit quantitative criteria [6-8]. The choice between these crite- ria is an ongoing point of discussion: implicit criteria are more easily applicable but generally lack definition, whereas explicit criteria are not unequivocally agreed upon and are often perceived as too inflexible [9-12]. In the State of Victoria (Australia), implicit categories of clin- ical urgency were identified and applied to all elective sur- gical registrations [13,14]. The Australian Government adopted the classification, delivering WLES national reports . An application of real time systems to surgi- cal waiting lists was described in 1999 by Davis and John- son, who developed a computerized model to get a "Patient's Eligibility Quotient" starting from a "Patient's Initial Quotient". In 2002, following the Australian experience, the Italian Government adopted implicit crite- ria to prioritize admission to elective surgery on the basis of four clinical Urgency-Related Groups (URGs) . Each URG was associated with a period of time within which admission should be provided ("Maximum Time Before Treatment", MTBT). Nevertheless, the application of URGs' proved difficult and Italian patients are generally admitted on a first-in first-out basis, taking into account broad and subjective views of urgency.
Abstract — We consider a population of dynamic agents (players). The state of each player evolves according to a linear stochastic differential equation driven by a Brownian motion and under the influence of a control and an adversarial disturbance. Every player minimizes a cost functional which involves quadratic terms on state and control plus a cross-coupling mean-field term measuring the congestion resulting from the collective behavior, which motivates the term “crowd-averse”. For this game we first illustrate the paradigm of robust mean-field games. Second, we provide a new approximate solution approach based on the extension of the state space and prove the existence of equilibria and their stability properties. Third, we provide a bound for the approximation introduced by the solution method. Simulations illustrating the approximate solution are presented.
Ex: According to the Bureau of Labor Statistics, the mean amount of money spent by a household on alcohol in the US is $565 per year. A church group wants to check this claim and took a random sample of 45 households and found that mean amount spent on alcohol per year was $520 with a standard deviation of $167. Test the church group’s claim that the mean amount of money spent on alcohol per year is less than $565. Use the _____________________ method.
Empirically investigating the e ff ect of patient census on total service rate and service rate per patient, Armony et al. (2011) observed evidence of a state dependent service rate (which in- volved both speed-up and slow-down mechanisms). Using 5 years of data from an Israeli hospital, the authors found that, as a function of patient census, the service rate first decreases then increases then again decreases, with some noise in the tails due to small sample sizes. Batt & Terwiesch (2012) identified the mechanisms that lead to state dependent services. Iden- tifying task reduction and early task initiation as speed-up mechanism and multitasking and interference as slow-down mechanisms, the authors obtained evidence of the existence of such mechanisms while analyzing 3 years of ED visit data from an urban teaching hospital using survival analysis and a count regression model. The authors also developed a discrete event simulation model, and used it to establish that ignoring state-dependent service times leads to modeling errors and could cause hospitals to over-invest in human and physical resources. In contrast, KC (2013) looked at the multitasking behavior of physicians in a busy ED using overall performance measures such as processing time, throughput rate, and output quality. Defining the busy period as the amount of time needed to serve a given number of patients without interruption, KC (2013) showed that busy period has a U-shaped response to the level of physician multitasking. The term “U-shaped relationship” means that an increase in the explanatory variable is associated with an initial reduction in the response, followed by an increase after a particular value of that explanatory variable.
Waitingtime is one of the dissatisfying factors that are frequently cited as a reason why patients switch to another hospital. Patient satisfaction is measurable through several dimensions like physical environment, empathy, communication, interaction, accessibility and technical quality of care.In this study the researcher assesses patients’ perception on the waitingtime to determine if this can also affect patients’ overall satisfaction.Samples of 110 inpatients above the age of eighteen were surveyed from the wards of selected government medical college hospitals in Kerala.Sample frame consist of inpatients of Thrissur, Kottayam and Kozhikode medical college hospitals. Simple random sampling technique is being used for this study. Patients report good perception on waitingtime to get the first aid treatment and waitingtime due to absence of doctor. Patients reported poor perception on the time spent at office for procedures. Perception of the patients on waitingtime is not varying with the age. Patients of different ward report different perceived waitingtime. Perceived waitingtime has correlation with the inpatients satisfaction but it is not influential to the overall patient satisfaction the relationship is not strong. Perception on waitingtime due to absence of doctor is more correlated to satisfaction.
A paper that has motivated a lot of recent work on asymptotic methods for the analysis of multi-server systems is due to Halfin and Whitt . In their paper, they perform an asymptotic analysis for M/M/N systems in the form of a simple diffusion process. It also provides useful insights about the scaling phenomena in these systems. This work has been extended in several ways: Jennings et. al  seem to be the first to have used the Halfin-Whitt regime in the context of call centers; they use this asymptotic regime to characterize staffing levels with time-varying demand. Flemming et al.  and Garnett et al.  have added the notion of abandonment (that is, customers renege after having waited in the queue for some time). Puhalskii and Reiman  have analyzed multi-class systems with renewal arrival and phase-type processing time distributions with and without priorities. A detailed asymptotic analysis of dimensioning rules for single class call centers has been done by Borst et al. . Finally, in a recent paper, Whitt  studies single-class multi-server systems in which arrival rates depend on system performance, including the scenario that leads to the limiting regime proposed by Halfin and Whitt in  that is also used here.
Expression of AMH is activated by SOX9 in the male sertoli cells and causes the irreversible regression of the Mullerian ducts (Taguchi et al., 1984). Because AMH expression is critical to sex differentiation at a specific time during fetal development, it appears to be tightly regulated by SF1, GATA factors, DAX1 and FSH (Shen et al., 1994; Nachtigal et al., 1998; Viger et al., 1998). Mutations in both the AMH gene and the type II AMH receptor have been shown to cause the persistence of Mullerian derivatives in males that are otherwise normally virilized (Belville et al., 1999). AMH expression also occurs in ovarian granulosa cells of females postpartum, and serves as a molecular biomarker for relative size of the ovarian reserve (Weenen et al., 2004). In humans, the number of cells in the follicular reserve can be used to predict timing of menopause (van Disseldorp et al., 2008). In bovine, AMH can be used for selection of females in multi-ovulatory embryo transfer programs by predicting the number of antral follicles developed to ovulation (Rico et al., 2011).
This paper identiﬁes two diﬀerent parametrized dynamic priority queue disciplines, earliest due date (EDD) based and head of line priority jump (HOL-PJ), which are found to be meanwaitingtime complete in two class M/G/1 queue. An explicit one-to-one non linear transformation is obtained between earliest due date and delay dependent priority pol- icy. Meanwaitingtime equivalence between these queue disciplines is established. Motivation behind the mean com- pleteness and equivalence results is discussed from optimal control perspective. Notion of minmax fairness is introduced and it is argued that a simple global FCFS policy is the only solution for minmax fairness problem in two class by exploiting completeness in the structure of EDD based dy- namic priority. Further, these completeness results are used to propose a simpler way for developing optimal control pol- icy in celebrated c/ρ rule for two class M/G/1 queues.
Triage decisions can be divided into primary and secondary decisions. Primary triage decisions relate to the assessment, allocation of a triage category and patient deposition whilst secondary triage decisions relate to the initiation of nursing interventions in order to expedite emergency care and promote patient comfort. The triage nurse is the first person that a patient encounters when presenting for emergency care. The triage nurse should be highly skilled in interpersonal and communication skills. She has a responsibility to be polite, professional and reassuring whilst eliciting the information he or she requires making a triage decision. (9) Patients and their families should have access to information regarding the triage process. This information should include a simple explanation of the principles of triage, the triage categories, how the patient has been categorized and their intended waitingtime. The reason for delays in waiting times, in case of the presence of seriously ill or injured patients. (10)
Queue is a waiting line or the act of joining a line. It is formed when the number of customers arriving is greater than the number of customers being served during a period of time. This study is essentially focused on the queuing system of healthcare centre operations. It is mainly based on the reducing of waitingtime of patients in the departments of Laboratory, Registration and Pharmacy at the Muthoot Medical Centre as these were the three departments that the hospital is facing long waiting times and complaints by the customers due to this issue.
(2.4) • The system may breakdown at random and the breakdowns are assumed to occur according to a Poisson stream with mean breakdown rate α > 0. Further we assume that once the system breakdown, the customer whose service is interrupted comes back to the head of queue.