Optimizing the performance of a blood analyser: Application of the set partitioning problem

The paper presents some models for optimizing the production rate of an automatic multitest blood analyser. A blood analysis may require one or more tests. The performance of the analyser depends on the test compositions of the analyses and the design of the analyser itself. The design can be changed. The optimal design can be determined by solving a set partitioning problem, given a representative sample of blood analyses

On a two-server finite queuing system with ordered entry and deterministic arrivals

Consider a two-server, ordered entry, queuing system with heterogeneous servers and finite waiting rooms in front of the servers. Service times are negative exponentially distributed. The arrival process is deterministic. A matrix solution for the steady state probabilities of the number of customers in the system is derived. The overflow probability will be used to formulate the stability condition of a closed-loop conveyor system with two work stations

On the expected number of assignments in reduced matrices for the linear assignment problem

A linear n × n assignment problem is considered for which the elements of the cost matrix are sampled from a continuous probability distribution. Based on the zero entries of the reduced matrix the expectation of the maximum number of initial assignments is determined for general n, as well as an asymptotic value for large n

Note on a tandem queue with delayed server release

We consider a tandem queue with two stations. The first station is an $s$-server queue with Poisson arrivals and exponential service times. After terminating his service in the first station, a customer enters the second station to require service at a single server, while in the meantime he is blocking his server in station 1 until he completes service in station 2, whereupon the server in station 1 is released. Two cases are considered. In the first case it is assumed that the service times in the second station are exponentially distributed. The solution of this model can be formulated using the matrix-geometric method. In the second case $s=2$ and, the service times are generally distributed. The model is analyzed using the supplementary variable technique, obtaining the relevant probability generating functions

A tandem queue with delayed server release

We consider a tandem queue with two stations. The rst station is an s-server queue with Poisson arrivals and exponential service times. After terminating his service in the rst station, a customer enters the second station to require service at an exponential single server, while in the meantime he is blocking his server in station 1 until he completes service in station 2, whereupon the server in station 1 is released. An analysis of the generating function of the simultaneous probability distribution of the queue lengths is given. An explicit expression for the stability condition and the solution for s = 2 is obtained

The optimal look-ahead policy for admission to a single server system

This paper considers a service system with a single server, finite waiting room, and a renewal arrival process. Customers who arrive while the server is busy are lost. Upon completing service, the server chooses between two actions:\ud either he immediately starts a new service, provided a customer is present, or\ud he admits the newly arrived customer to the system, but delays service pending\ud the next arrival, whereupon he again chooses between these two actions. This\ud process continues until either the system is full or a new service is started.\ud Once a service has been started, all customers who arrive while the server is busy are lost. We assume that at each decision epoch the server knows the arrival epoch of the first arriving customer. We show that there exists an optimal control-limit policy that minimizes the average expected idle time per customer served (equivalently, maximizes the average number of customers served per unit of time). The special case of Poisson arrivals leads to an explicit expression for this delay that generalizes exisiting results

Look-ahead policies for admission to a single server loss system

Consider a single server loss system in which the server, being idle, may reject or accept an arriving customer for service depending on the state at the arrival epoch. It is assumed that at every arrival epoch the server knows the service time of the arriving customer, the arrival time of the next customer and the service time. The server gets a fixed reward for every customer admitted to the system. The form of an optimal stationary policy is investigated for the discounted and average reward cases

On a random interval graph and the maximum throughput rate in the system GI/G/1/0

The paper gives an explicit expression for the expectation of the maximum attainable fraction of served customers in the long run for the single-server loss system GI/GI1/0, under the assumption of perfect information regarding the sequences {X,, i = 1, 2, - - - } and {Yi, i = 1, 2, ..--- } of interarrival times and service times, respectively. A heavy traffic result for this fraction is obtained for the system GI/M/1/0. The general result is based on an analysis of the random interval graph corresponding to the random intervals {[Ti, T1 + Y), i = 1,2,... }, in which { I} denotes the sequence of arrival epochs

Can ACE2 expression explain SARS-CoV-2 infection of the respiratory epithelia in COVID-19?

Infection with severe acute respiratory syndrome coronavirus‐2 (SARS‐CoV‐2) leads to coronavirus disease 2019 (COVID‐19), which poses an unprecedented worldwide health crisis, and has been declared a pandemic by the World Health Organization (WHO) on March 11, 2020. The angiotensin converting enzyme 2 (ACE2) has been suggested to be the key protein used by SARS‐CoV‐2 for host cell entry. In their recent work, Lindskog and colleagues (Hikmet et al, 2020) report that ACE2 is expressed at very low protein levels—if at all—in respiratory epithelial cells. Severe COVID‐19, however, is characterized by acute respiratory distress syndrome and extensive damage to the alveoli in the lung parenchyma. Then, what is the role of the airway epithelium in the early stages of COVID‐19, and which cells need to be studied to characterize the biological mechanisms responsible for the progression to severe disease after initial infection by the novel coronavirus