An Interpretation of Non-Preemptive Priority Fuzzy Queuing Model with Asymmetrical Service Rates

This paper presents Non-Preemptive priority fuzzy queuing model with asymmetrical service rates. Arrival rate and service rate are taken to be hexagonal, heptagonal, and octagonal fuzzy numbers. Here an interpretation is given to determine the performance measures by applying a new ranking technique through which the fuzzy values are reduced to the crisp values. This ranking technique has the benefit of being precise and relevant compared to other methods such as alpha-cut method and LR method. The main intention is to evaluate the fuzziness before the performance measures are processed by utilizing the regular queueing hypothesis. Three numerical examples are exhibited to show the validity implementation of the methodology.

Stability, Memory, and Messaging Trade-Offs in Heterogeneous Service Systems

We consider a heterogeneous distributed service system consisting of n servers with unknown and possibly different processing rates. Jobs with unit mean arrive as a renewal process of rate proportional to n and are immediately dispatched to one of several queues associated with the servers. We assume that the dispatching decisions are made by a central dispatcher with the ability to exchange messages with the servers and endowed with a finite memory used to store information from one decision epoch to the next, about the current state of the queues and about the service rates of the servers. We study the fundamental resource requirements (memory bits and message exchange rate) in order for a dispatching policy to be always stable. First, we present a policy that is always stable while using a positive (but arbitrarily small) message rate and [Formula: see text] bits of memory. Second, we show that within a certain broad class of policies, a dispatching policy that exchanges [Formula: see text] messages per unit of time, and with [Formula: see text] bits of memory, cannot be always stable.

Examining Health Service Rates Among Residents of Retirement Homes and Other Older Adult Populations in Ontario, Canada: A Population-Based Cohort Study

Background: There are no standardized reporting systems or assessments specific to residents of retirement homes in North America. As such, little is known about these older adults as a distinct population. We created a new population-level cohort of residents of retirement homes and examined their health service rates relative to other older adult populations. Methods: We conducted a population-based retrospective cohort study in Ontario, Canada in 2018. The postal codes of all licensed retirement homes (n = 757) were classified and linked to individual-level health system administrative data to derive a cohort of residents of retirement homes. A generalized linear model with a gamma distribution and log link function was used to model rates of emergency department visits, hospitalizations, alternate levels of care (ALC) days, primary care visits, and specialist physician visits. Results: Residents of retirement homes comprised two percent of the older adult population in Ontario (n = 54,773; 2.3%). After adjustment for relevant characteristics, residents of retirement homes had 10 times the rate of emergency department visits (Relative Rate [RR] 10.02, 95% Confidence Interval [CI] 9.83 to 10.21), 20 times the rate of hospitalizations (RR 20.43, 95% CI 20.08 to 20.78), and 44 times the rate ALC days (RR 43.91, 95% CI 43.28 to 44.54) compared to community-dwelling older adults. Interpretation: Residents of retirement homes are a distinct older adult population with high rates of hospital-based care. Our findings contribute to policy debates about the provision of health care in privately operated congregate care settings for older adults.

A Multi-Objective Mathematical Model for Real-Time Employee Assignment in the Service Industry

The American economy has shifted toward services since the 1980s. The service industry is an important part of economy and is growing quickly in the last three decades. It is more human-capital intensive than the manufacturing sector and there is a shortage of highly-skilled workforce. One solution to this problem is to improve the efficiency through optimization. Because demand in the service industry changes constantly, it is a great challenge to determine the number of employees and their tasks to improve customer service while reducing cost. This article develops a multi-objective mixed-integer linear programming model to dynamically assign employees to different workstations in real time. A case study of the model is solved in less than one second and its pareto optimal solutions determine the number of employees who are assigned to each workstation and the expected customer service times. The mathematical model is robust and provides optimal employee assignment and service rates for workstations in many situations.

Variational inference for Markovian queueing networks

Queueing networks are stochastic systems formed by interconnected resources routing and serving jobs. They induce jump processes with distinctive properties, and find widespread use in inferential tasks. Here, service rates for jobs and potential bottlenecks in the routing mechanism must be estimated from a reduced set of observations. However, this calls for the derivation of complex conditional density representations, over both the stochastic network trajectories and the rates, which is considered an intractable problem. Numerical simulation procedures designed for this purpose do not scale, because of high computational costs; furthermore, variational approaches relying on approximating measures and full independence assumptions are unsuitable. In this paper, we offer a probabilistic interpretation of variational methods applied to inference tasks with queueing networks, and show that approximating measure choices routinely used with jump processes yield ill-defined optimization problems. Yet we demonstrate that it is still possible to enable a variational inferential task, by considering a novel space expansion treatment over an analogous counting process for job transitions. We present and compare exemplary use cases with practical queueing networks, showing that our framework offers an efficient and improved alternative where existing variational or numerically intensive solutions fail.

The Stability Analysis of a Double-X Queuing Network Occurring in the Banking Sector

We model a common teller–customer interaction occurring in the Ghanaian banking sector via a Double-X queuing network consisting of three single servers with infinite-capacity buffers. The servers are assumed to face independent general renewal of customers and independent identically distributed general service times, the inter-arrival and service time distributions being different for each server. Servers, when free, help serve customers waiting in the queues of other servers. By using the fluid limit approach, we find a sufficient stability condition for the system, which involves the arrival and service rates in the form of a set of inequalities. Finally, the model is validated using an illustrative example from a Ghanaian bank.