Approximations and Optimal Control for State-Dependent Limited Processor Sharing Queues

The paper studies approximations and control of a processor sharing (PS) server where the service rate depends on the number of jobs occupying the server. The control of such a system is implemented by imposing a limit on the number of jobs that can share the server concurrently, with the rest of the jobs waiting in a first-in-first-out (FIFO) buffer. A desirable control scheme should strike the right balance between efficiency (operating at a high service rate) and parallelism (preventing small jobs from getting stuck behind large ones). We use the framework of heavy-traffic diffusion analysis to devise near optimal control heuristics for such a queueing system. However, although the literature on diffusion control of state-dependent queueing systems begins with a sequence of systems and an exogenously defined drift function, we begin with a finite discrete PS server and propose an axiomatic recipe to explicitly construct a sequence of state-dependent PS servers that then yields a drift function. We establish diffusion approximations and use them to obtain insightful and closed-form approximations for the original system under a static concurrency limit control policy. We extend our study to control policies that dynamically adjust the concurrency limit. We provide two novel numerical algorithms to solve the associated diffusion control problem. Our algorithms can be viewed as “average cost” iteration: The first algorithm uses binary-search on the average cost, while the second faster algorithm uses Newton-Raphson method for root finding. Numerical experiments demonstrate the accuracy of our approximation for choosing optimal or near-optimal static and dynamic concurrency control heuristics.

Discrete event simulation applied to single queue management: a case study at a bank agency

Capacity and queue management are currently used in financial institutions. With decreasing bank units due to internet services, research in this field has focused on improving to utilize their employees efficiently and achieve service excellence. In developing countries like Brazil, the customer has become more bank-accounted due to government and labor requirements, such as the wage credit became mandatory in the wage account. The paper's aim is motivated by a real-life case study to simulate discrete events to improve queue management at a Brazilian bank branch with the Arena software simulation environment. The simulation model was designed, tested, and applied considering the Discrete Event Simulation (DES) replication for queuing strategies on a real-world banking scenario. The arrival and service times were collected from 115 customers in Ferraz de Vasconcelos/SP city. It was performed in version 15.10 (2018) of the Arena software, with processor Intel core i3 CPU dual-core 3.07 GHz and 8GB of RAM. The results indicate that the bank agency should consider providing 9 to 11 operators to attend customers considering the arrival and service rate.

Analysis and optimisation of a M/M/1/WV queue with Bernoulli schedule vacation interruption and customer’s impatience

In this investigation, we establish a steady-state solution of an infinite-space single-server Markovian queueing system with working vacation (WV), Bernoulli schedule vacation interruption, and impatient customers. Once the system becomes empty, the server leaves the system and takes a vacation with probability p or a working vacation with probability 1 − p, where 0 ≤ p ≤ 1. The working vacation period is interrupted if the system is non empty at a service completion epoch and the server resumes its regular service period with probability 1 − q or carries on with the working vacation with probability q. During vacation and working vacation periods, the customers may be impatient and leave the system. We use a probability generating function technique to obtain the expected number of customers and other system characteristics. Stochastic decomposition of the queueing model is given. Then, a cost function is constructed by considering different cost elements of the system states, in order to determine the optimal values of the service rate during regular busy period, simultaneously, to minimize the total expected cost per unit time by using a quadratic fit search method (QFSM). Further, by taking illustration, numerical experiment is performed to validate the analytical results and to examine the impact of different parameters on the system characteristics.

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.

Analysis of Patient Characteristics, Financing of Actions and Diagnosis of Disease in BPJS Patients

Background: Dental and oral health services are a form of professional service that is an integral part of health services for the community, families or individuals3. Implementation of a dental specialist clinic at the 2nd health facility is a referral from the health facility 1 All financing is borne by BPJS with INA CBGS financing. Purpose: This study aims to determine patient characteristics and disease diagnosis of BPJS patients in specialist dental clinic in Islamic Hospital Surabaya. Methods: This study used a qualitative research method with a descriptive analytic study. From the BPJS TXT data for January - December 2019, there were 7153 patient visits at the dental specialist clinic of the Islamic Hospital in Surabaya, the TXT data is data issued by the BPJS as a result of purification of billing file data recognized by the BPJS. Results: Based on the results of the study, it was found that most of the patients were male, with the largest age ranges being <25 years and> 50 years. The implementation of the tariff difference between INA CBGS and the fare difference of the Islamic Hospital in Surabaya is - 128,091,924 with an average of - 17,907 / patient. Of the total TXT, the largest financing of the INA CBGS tariff is the doctor service rate with a percentage of 54.90%. Conclusion: the implementation of BPJS examination of specialist dental polyclinic at RS Islam Surabaya did not give the maximum benefit.

Probabilistic Set Covering Location Problem in Congested Networks

This paper focuses on designing a facility network, taking into account that the system may be congested. The objective is to minimize the overall fixed and service capacity costs, subject to the constraints that for any demand the disutility from travel and waiting times (measured as the weighted sum of the travel time from a demand to the facility serving that demand and the average waiting time at the facility) cannot exceed a predefined maximum allowed level (measured in units of time). We develop an analytical framework for the problem that determines the optimal set of facilities and assigns each facility a service rate (service capacity). In our setting, the consumers would like to maximize their utility (minimize their disutility) when choosing which facility to patronize. Therefore, the eventual choice of facilities is a user-equilibrium problem, where at equilibrium, consumers do not have any incentive to change their choices. The problem is formulated as a nonlinear mixed-integer program. We show how to linearize the nonlinear constraints and solve instead a mixed-integer linear problem, which can be solved efficiently.

Study on Transient Queue-Size Distribution in the Finite-Buffer Model with Batch Arrivals and Multiple Vacation Policy

The transient behavior of the finite-buffer queueing model with batch arrivals and generally distributed repeated vacations is analyzed. Such a system has potential applications in modeling the functioning of production systems, computer and telecommunication networks with energy saving mechanism based on cyclic monitoring the queue state (Internet of Things, wireless sensors networks, etc.). Identifying renewal moments in the evolution of the system and applying continuous total probability law, a system of Volterra-type integral equations for the time-dependent queue-size distribution, conditioned by the initial buffer state, is derived. A compact-form solution for the corresponding system written for Laplace transforms is obtained using an algebraic approach based on Korolyuk’s potential method. An illustrative numerical example presenting the impact of the service rate, arrival rate, initial buffer state and single vacation duration on the queue-size distribution is attached as well.

Finite M/M/1 retrial model with changeable service rate

The article deals with M/M/1 -type retrial queueing system with finite orbit. It is supposedthat service rate depends on the loading of the system. The explicit formulae for ergodicdistribution of the number of customers in the system are obtained. The theoretical results areillustrated by numerical examples.

Queue Management Benchmark for Modelling Patients' Flow in Nigerian Public Hospitals

Although queue management in hospitals is widely researched, little is known about the benchmark for modelling patients flow in terms of the optimal number of servers required for effective service delivery. This study applied the queuing theory to the Nigerian public hospitals by setting a benchmark for modelling patients flow. A mixture of survey and observation was adopted to garner data for 30 days from patients in six public hospitals in Nigeria. Data were subjected to performance analysis via the Temporary Ordered Routine Algorithm. The computed performance values were further compared with their acceptable benchmarks for multi-server queues through the General Purpose System Simulator. We found the queuing system in the select hospitals not in congruence with the system performance benchmark; the mean service rate in each facility was low compared to the mean arrival rate; and the simulated number of doctors for were below the modelled benchmark. Managerial implications of findings were discussed.