Correlated queues with service times depending on inter-arrival times

2021 ◽  
Author(s):  
Weimin Dai ◽  
Jian-Qiang Hu
Keyword(s):  
Arrival Times ◽  
Service Times

scholarly journals Assessment of patients waiting and service times in the ophthalmology clinic of a public tertiary hospital in Nigeria

2020 ◽  
Vol 54 (4) ◽  
pp. 231-237
Author(s):  
Lateefat B. Olokoba ◽  
Kabir A. Durowade ◽  
Feyi G. Adepoju ◽  
Abdulfatai B. Olokoba
Keyword(s):  
Waiting Time ◽  
Waiting Times ◽  
Sampling Technique ◽  
Tertiary Hospital ◽  
Cross Sectional Study ◽  
Ethical Review ◽  
Cross Sectional ◽  
Arrival Times ◽  
The Mean ◽  
Service Times

Introduction: Long waiting time in the out-patient clinic is a major cause of dissatisfaction in Eye care services. This study aimed to assess patients’ waiting and service times in the out-patient Ophthalmology clinic of UITH. Methods: This was a descriptive cross-sectional study conducted in March and April 2019. A multi-staged sampling technique was used. A timing chart was used to record the time in and out of each service station. An experience based exit survey form was used to assess patients’ experience at the clinic. The frequency and mean of variables were generated. Student t-test and Pearson’s correlation were used to establish the association and relationship between the total clinic, service, waiting, and clinic arrival times. Ethical approval was granted by the Ethical Review Board of the UITH. Result: Two hundred and twenty-six patients were sampled. The mean total waiting time was 180.3± 84.3 minutes, while the mean total service time was 63.3±52.0 minutes. Patient’s average total clinic time was 243.7±93.6 minutes. Patients’ total clinic time was determined by the patients’ clinic status and clinic arrival time. Majority of the patients (46.5%) described the time spent in the clinic as long but more than half (53.0%) expressed satisfaction at the total time spent at the clinic. Conclusion: Patients’ clinic and waiting times were long, however, patients expressed satisfaction with the clinic times.

scholarly journals An invariant distribution for the G/G/1 queueing operator

1990 ◽  
Vol 22 (1) ◽  
pp. 254-256 ◽  
Author(s):  
Nicholas Bambos ◽  
Jean Walrand
Keyword(s):  
Invariant Distribution ◽  
Arrival Times ◽  
Service Times

We consider the G/G/1 queue as an operator that maps inter-arrival times to inter-departure times of points, given the service times. For arbitrarily fixed statistics of service times, we are interested in the existence of distributions of inter-arrival times that induce identical distributions on the inter-departure times. In this note we prove, by construction, the existence of one of such distribution.

MULTI-CHANNEL FUZZY QUEUING SYSTEMS AND MEMBERSHIP FUNCTIONS OF RELATED FUZZY SERVICES AND FUZZY INTER-ARRIVAL TIMES

2008 ◽  
Vol 25 (05) ◽  
pp. 697-713 ◽  
Author(s):  
ÖZLEM AYDIN ◽  
AYŞEN APAYDIN
Keyword(s):  
Membership Function ◽  
Measurement Errors ◽  
Waiting Times ◽  
Membership Functions ◽  
Queuing Systems ◽  
Queuing Model ◽  
Arrival Times ◽  
Queuing Models ◽  
Service Times ◽  
The One

Queuing models need well defined knowledge on arrivals and service times. However, in real applications, because of some measurement errors or some loss of information, it is hard to achieve deterministic knowledge. Non-deterministic knowledge interferes or complicates analysis of the queuing model. Additionally, when the customers are asked about their impressions on waiting times or service times, mostly the answers are linguistic expressions like "I waited too much", "service was fast", and that the responses are. Linguistic statements and ill defined data make the sense of imprecision in the model. In this study, arrivals and service times are defined as fuzzy numbers in order to represent this imprecision. Fuzzy multi-channel queuing systems and membership functions are introduced in defining the arrivals and service times. Besides, a new membership function based on a probability function is studied. Fuzzy queuing characteristics are calculated via different membership functions and the results are compared on simulations. Among models it is found that, Generalized Beta Distribution membership function is the one that minimized the queuing characteristics.

A note on the queueing system GI/G/∞

1968 ◽  
Vol 64 (2) ◽  
pp. 477-479 ◽  
Author(s):  
D. N. Shanbhag
Keyword(s):  
Distribution Function ◽  
Service Time ◽  
Queueing System ◽  
Expected Value ◽  
Arrival Times ◽  
Service Times

Consider a queueing system GI/G/∞ in which (i) the inter-arrival times are distributed with distribution function A(t) (A(O +) = 0) (ii) the service times have distribution function B(t) such that the expected value of the service time is β(>∞).

On the distribution of queueing times

1953 ◽  
Vol 49 (3) ◽  
pp. 449-461 ◽  
Author(s):  
Walter L. Smith
Keyword(s):  
Single Server ◽  
Theoretical Studies ◽  
Single Server Queue ◽  
Hypothetical Model ◽  
Arrival Times ◽  
Present Treatment ◽  
Server Queue ◽  
Service Times

The hypothetical model that we shall be considering in this paper is referred to as the single-server queue, and the details of this model are given in a recent paper by Lindley(5). The present treatment involves exactly the same assumptions as Lindley has given already, and we refer to his paper for a rigorous statement of them. Briefly, we shall be assuming general independent service times and general independent input or arrival times. Theoretical studies of the single-server queue are capable of wide applications, many of which are described in a paper by Kendall (4) and in the discussion to that paper.

scholarly journals An invariant distribution for the G/G/1 queueing operator

1990 ◽  
Vol 22 (01) ◽  
pp. 254-256 ◽  
Author(s):  
Nicholas Bambos ◽  
Jean Walrand
Keyword(s):  
Invariant Distribution ◽  
Arrival Times ◽  
Service Times

We consider the G/G/1 queue as an operator that maps inter-arrival times to inter-departure times of points, given the service times. For arbitrarily fixed statistics of service times, we are interested in the existence of distributions of inter-arrival times that induce identical distributions on the inter-departure times. In this note we prove, by construction, the existence of one of such distribution.

scholarly journals Optimal Server Selection in a Queueing Loss Model with Heterogeneous Exponential Servers, Discriminating Arrivals, and Arbitrary Arrival Times

2014 ◽  
Vol 51 (3) ◽  
pp. 880-884 ◽  
Author(s):  
Sheldon M. Ross
Keyword(s):  
Arrival Process ◽  
Loss System ◽  
Binary Variables ◽  
Indicator Variable ◽  
Loss Model ◽  
Arrival Times ◽  
Independent Variables ◽  
Server Selection ◽  
Service Times

We consider a multiple server queueing loss system where the service times of server i are exponential with rate μi, where μi decreases in i. Arrivals have associated vectors (X1, …, Xn) of binary variables, with Xi = 1 indicating that server i is eligible to serve that arrival. Arrivals finding no idle eligible servers are lost. Letting Ij be the indicator variable for the event that the jth arrival enters service, we show that, for any arrival process, the policy that assigns arrivals to the smallest numbered idle eligible server stochastically maximizes the vector (I1, …, Ir) for every r if the eligibility vector of arrivals is either (a) exchangeable, or (b) a vector of independent variables for which P(Xi = 1) increases in i.

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