Moment formulas for the Markov renewal branching process

1976 ◽  
Vol 8 (4) ◽  
pp. 690-711 ◽  
Author(s):  
Marcel F. Neuts
Keyword(s):  
Steady State ◽  
Numerical Computation ◽  
Busy Period ◽  
Branching Process ◽  
Queueing Models ◽  
Absorption Time ◽  
The Mean ◽  
The Moment

There are many queueing models in which there appears a semi-Markov matrix G(·), whose entries are absorption-time distributions in a Markov renewal branching process. The role of G(·) is similar to that of the busy period in the simple M/G/1 model. The computation of various quantities associated with G(·) is however much more complicated. The moment matrices, and particularly the mean matrix of G(·), are essential in the construction of general and mathematically well-justified algorithms for the steady-state distributions of such queues.This paper discusses the moment matrices of G(·) and algorithms for their numerical computation. Its contents are basic to the algorithmic solutions to several queueing models, which are to be presented in follow-up papers.

Moment formulas for the Markov renewal branching process

1976 ◽  
Vol 8 (04) ◽  
pp. 690-711 ◽  
Author(s):  
Marcel F. Neuts
Keyword(s):  
Steady State ◽  
Numerical Computation ◽  
Busy Period ◽  
Branching Process ◽  
Queueing Models ◽  
Absorption Time ◽  
The Mean ◽  
The Moment

There are many queueing models in which there appears a semi-Markov matrix G(·), whose entries are absorption-time distributions in a Markov renewal branching process. The role of G(·) is similar to that of the busy period in the simple M/G/1 model. The computation of various quantities associated with G(·) is however much more complicated. The moment matrices, and particularly the mean matrix of G(·), are essential in the construction of general and mathematically well-justified algorithms for the steady-state distributions of such queues. This paper discusses the moment matrices of G(·) and algorithms for their numerical computation. Its contents are basic to the algorithmic solutions to several queueing models, which are to be presented in follow-up papers.

The second moments of the absorption times in the Markov renewal branching process

1978 ◽  
Vol 15 (04) ◽  
pp. 707-714 ◽  
Author(s):  
Marcel F. Neuts
Keyword(s):  
Busy Period ◽  
Branching Process ◽  
Queueing Models ◽  
Explicit Formulas ◽  
Absorption Time ◽  
Iterative Computation ◽  
Second Moments ◽  
Number Of Customers

We derive explicit formulas for the second moments of the absorption time matrices in the Markov renewal branching process. These formulas may easily be computationally implemented and are useful in the iterative computation of the semi-Markov matrices, which give the distributions of the duration and of the number of customers served in a busy period of a great variety of complex queueing models.

The second moments of the absorption times in the Markov renewal branching process

1978 ◽  
Vol 15 (4) ◽  
pp. 707-714 ◽  
Author(s):  
Marcel F. Neuts
Keyword(s):  
Busy Period ◽  
Branching Process ◽  
Queueing Models ◽  
Explicit Formulas ◽  
Absorption Time ◽  
Iterative Computation ◽  
Second Moments ◽  
Number Of Customers

We derive explicit formulas for the second moments of the absorption time matrices in the Markov renewal branching process. These formulas may easily be computationally implemented and are useful in the iterative computation of the semi-Markov matrices, which give the distributions of the duration and of the number of customers served in a busy period of a great variety of complex queueing models.

scholarly journals Sentinel Node Biopsy for Conjunctival Melanoma; Single Centre Experience and Review of Current Literature

2021 ◽  
Vol 28 ◽  
pp. 107327482110421
Author(s):  
Barbara Peric ◽  
Spela Leiler ◽  
Gregor Hawlina ◽  
Boris Jancar ◽  
Marko Snoj ◽  
...  
Keyword(s):  
Overall Survival ◽  
Single Centre ◽  
Node Biopsy ◽  
Single Centre Experience ◽  
Observational Cohort ◽  
The Mean ◽  
The Moment ◽  
Retrospective Observational Cohort Study

Purpose To evaluate the role of sentinel lymph node (SLN) biopsy in patients with conjuctival melanoma (CjM). Study design Retrospective observational cohort study and literature review. Subjects Slovenian patients with CjM are included in the study. Methods Prospectively collected data of CjM patients treated from June 2005 to December 2016 were retrospectively analyzed. Main outcome measures The numbers of SLN biopsy procedures, positive and false positive SLN, and local and regional relapses have been described together with overall survival. Results From June 2005 until December 2016, 24 patients with CjM were treated. The median follow-up time was 65.3 months. The mean Breslow thickness was 1.5 mm (sd = 1.8 mm), and ulceration was present in 29% of cases. Altogether, 14/24 (58%) SLN biopsy procedures were performed. SLN was positive in 2/14 (14%) cases. The estimated 5-year overall survival (OS) of the group was 72.5%, with a median survival of 151 months (95% CI 77–224). From January 2013 to January 2020, five (5/140, 3%) authors reported results comparable to our study. Conclusion Our results confirm that CjM is a rare disease with approximately 14% of positive SLN. At the moment, there are no firm conclusions regarding who would benefit most from SLN biopsy or whether or not CLND should be offered. Data from literature emphasize the need for consistent and uniform staging and future multicentric studies.

scholarly journals Reservicing some customers inM/G/1queues under three disciplines

2004 ◽  
Vol 2004 (32) ◽  
pp. 1715-1723 ◽  
Author(s):  
M. R. Salehi-Rad ◽  
K. Mengersen ◽  
G. H. Shahkar
Keyword(s):  
Steady State ◽  
Generating Function ◽  
Production Line ◽  
Busy Period ◽  
Probability Generating Function ◽  
Idle Period ◽  
The Mean ◽  
The Moment ◽  
State Size

Consider anM/G/1production line in which a production item is failed with some probability and is then repaired. We consider three repair disciplines depending on whether the failed item is repaired immediately or first stockpiled and repaired after all customers in the main queue are served or the stockpile reaches a specified threshold. For each discipline, we find the probability generating function (p.g.f.) of the steady-state size of the system at the moment of departure of the customer in the main queue, the mean busy period, and the probability of the idle period.

scholarly journals SAT0267 ROLE OF AGGRESSIVE IMMUNOSUPPRESSION ON SUBGLOTTIC STENOSIS IN GRANULOMATOSIS WITH POLYANGIITIS: RETROSPECTIVE ANALYSIS OF A MONOCENTRIC COHORT

2020 ◽  
Vol 79 (Suppl 1) ◽  
pp. 1076.1-1077
Author(s):  
L. Moroni ◽  
L. Giudice ◽  
G. A. Ramirez ◽  
S. Sartorelli ◽  
A. Cariddi ◽  
...  
Keyword(s):  
Medical Treatment ◽  
Clinical Characteristics ◽  
Granulomatosis With Polyangiitis ◽  
Balloon Catheter ◽  
Subglottic Stenosis ◽  
Damage Accrual ◽  
The Mean ◽  
The One

Background:Subglottic stenosis (SGS) is defined as airway narrowing below the vocal cords and is a common and potentially life-threatening manifestation of Granulomatosis with Polyangiitis (GPA), with an estimated prevalence of 16-23% (1). Balloon catheter dilation is effective in GPA-related SGS, but relapses are frequent. Little is known about the role of immunosuppression in this setting.Objectives:to analyse the clinical characteristics of a monocentric GPA cohort, describe phenotype differences among patients with and without SGS and investigate the role of surgical and medical treatments on relapse risk and general outcome.Methods:Biopsy-proven patients with SGS were identified by review of medical charts among a cohort of patients with GPA, classified according to the algorithm of the European Medicine Agency (2). The clinical characteristics of patients with SGS were retrospectively collected over a median follow-up time of 15.9 years and compared to those of patients without SGS.Results:Fourteen patients with SGS-GPA were identified, with a female to male ratio of 1:1 and a prevalence of 29.2% among the cohort. The mean ± SD age at GPA onset was 30.8 ± 14.4 years, with a mean time from GPA diagnosis to SGS onset of 4.7 ± 4.2 years. ANCA were positive in 78.6% (54.0% anti-PR3, 18.1% anti-MPO and 27.9% IFI only). The mean Birmingham Vasculitis Activity Score (BVAS) at onset was 10.0 ± 5.6. The main clinical manifestations associated with SGS were crusty rhinitis (100%), sinusitis (78%), pulmonary disease (72.7%), otitis/mastoiditis (50%), glomerulonephritis (42.9%), orbital pseudotumor (28.6%). Six patients (42.9%) received medical treatment only, other six (42.9%) had one to three balloon dilations and two (14.2%) underwent four or more procedures. Eight patients had no SGS relapse (maximum one dilation) and they all received immunosuppression with rituximab (RTX), cyclophosphamide (CYC) or azathioprine (AZA). All patients who received no immunosuppression, methotrexate (MTX) or mycophenolate (MMF) had at least one relapse. Patients treated with MTX or MMF had a mean relapse-free survival of 13.1 months, which was comparable to the one of patients not receiving medical treatment (40.2 months; p=NS) and shorter than the one of patients receiving CYC or RTX (153.2 months; p=0.032). CYC use also inversely correlated with the number of surgical procedures (r=-0.691, p=0.006). Compared to patients without SGS (31 consecutive patients with at least 4 years of follow-up), patients with SGS-GPA had an earlier disease onset (mean age 30.8 vs 50.4 years; p<0.001), but with lower BVAS (mean 10.0 vs 15.3; p=0.013) and showed a higher prevalence of crusty rhinitis (100% vs 67.7%; p=0.019). No difference was observed in damage accrual over time between the two groups.Conclusion:Subglottic stenosis is highly prevalent in patients with GPA and may define a milder disease subset occurring more frequently in younger patients. MTX and MMF might be insufficient to prevent SGS relapses requiring balloon dilation. Aggressive immunosuppression (CYC or RTX) might have a non-redundant role in this setting and reduce the risk of relapses.References:[1]Quinn KA, et al. Subglottic stenosis and endobronchial disease in granulomatosis with polyangiitis. Rheumatology 2019; 58 (12), 2203-2211.[2]Watts R, et al. Development and validation of a consensus methodology for the classification of the ANCA associated vasculitides and polyarteritis nodosa for epidemiological studies. Ann Rheum Dis 2007; 66: 222-7.Disclosure of Interests:Luca Moroni: None declared, Laura Giudice: None declared, Giuseppe Alvise Ramirez: None declared, Silvia Sartorelli: None declared, adriana cariddi: None declared, Angelo Carretta: None declared, Enrica Bozzolo: None declared, Lorenzo Dagna Grant/research support from: The Unit of Immunology, Rheumatology, Allergy and Rare Diseases (UnIRAR) received unresctricted research/educational grants from Abbvie, Bristol-Myers Squibb, Celgene, Janssen, Merk Sharp & Dohme, Mundipharma Pharmaceuticals, Novartis, Pfizer, Roche, Sanofi-Genzyme, and SOBI., Consultant of: Prof Lorenzo Dagna received consultation honoraria from Abbvie, Amgen, Biogen, Bristol-Myers Squibb, Celltrion, Novartis, Pfizer, Roche, Sanofi-Genzyme, and SOBI.

scholarly journals THU0517 THE ROLE OF ULTRASOUND-DEFINED SYNOVITIS GRADE I IN PATIENTS PRESENTING WITH INFLAMMATORY ARTHRALGIA, A RETROSPECTIVE STUDY

2020 ◽  
Vol 79 (Suppl 1) ◽  
pp. 497.2-497
Author(s):  
J. Arroyo Palomo ◽  
M. Arce Benavente ◽  
C. Pijoan Moratalla ◽  
B. A. Blanco Cáceres ◽  
A. Rodriguez
Keyword(s):  
Rheumatoid Arthritis ◽  
Inflammatory Arthritis ◽  
Statistical Tests ◽  
Median Number ◽  
Painful Joint ◽  
Significant Difference ◽  
The Mean ◽  
Specialized Unit

Background:Musculoeskeletal ultrasound (MSUS) is frequently used in several rheumatology units to detect subclinical inflammation in patients with joint symptoms suspected for progression to inflammatory arthritis (IA). Synovitis grade I (EULAR-OMERACT combined score) is known to be a casual finding in healthy individuals, but studies headed to unravel its possible role on rheumatic diseases are sparse.Objectives:To investigate the correlation between synovitis grade I, and the diagnosis of IA made after a year follow-up period since MSUS findings, in patients of an MSUS-specialized unit of a Rheumatology Department.Methods:We conducted a descriptive, retrospective and unicentric study. 30 patients were selected from the MSUS-specialized unit of our Rheumatology Department from July-18 to January-19. Patients presenting synovitis grade 0 (exclusively), 2 and/or 3 on combined score were excluded. Data collection at baseline included age, sex, immunological profile and previous physical examination to the MSUS findings, as well as the diagnosis made by the rheumatologist in 1-year visit follow-up: dividing the patient sample into two groups: those who were diagnosed with IA and those not. Non-parametric statistical tests for comparing means were used.Results:The mean age was 51,6 years and 70% were females. 6 (20%) patients were diagnosed with inflammatory arthritis after a year follow-up: 2 (4,8%) psoriatic arthritis, 1 (3,3%) undifferentiated arthritis, 1 (3,3%) rheumatoid arthritis, 1 (3,3%) Sjögren’s syndrome. Non-inflammatory arthropathies were also found 24 (80%), of which, 12 (40%) were non-specific arthralgias and 8 (19%) osteoarthritis.In the group of patients who did not developed an IA the mean C-reactive protein (CPR) value was 3,12 mg/L and erythrocyte sedimentation rate (ESR) was 8,2 mm; all of them were rheumatoid factor (RF) positive and ACPA-negative except one patient. 5 (31,3%) patients presented low antinuclear antibodies (ANAs) levels. In those who HLA B-27 and Cw6 were tested (4,25%); both were negative except for one that was HLA B-27 positive. The median number of swollen and painful joint count was 0, and the mean of joints with MSUS involvement was 3,5; the mean involved metacarpophalangeal (MCP) joints was 1,83; proximal interphalangeal (PIP) joints was 1,48 and distal interphalangeal (DIP) joints 0,21.Among the group of patients that developed an IA the mean of CPR and ESR was 9,27 mg/L and 14,17 mm respectively; 2 (33%) patients were RF- positive, and 1 ACPA-positive. ANAs were positive in 3 cases (50%). The median of swollen joint count was 2 and for painful joint count was 0, the median of joints with MSUS involvement was 4,5. The mean of MSUS involvement was for MCP, PIP and DIP joints: 1,67, 2 and 0. Comparing the means of CPR values in the two groups with Student’s t-test we obtained a statistically significant difference (p=0,023). No other significant differences were found.Conclusion:Despite the limitations and possible statistical bias, the presence of MSUS-defined synovitis grade I and elevated CRP levels could be related to further diagnoses of inflammatory arthropathy. Besides, the absence of synovitis in DIP joints might have a diagnostic role. Normal physical exploration and normal levels of CRP might suggest low MSUS value. However, further research is needed to clarify the role of MSUS-defined synovitis grade I.References:[1]D’Agostino MA et al. Scoring ultrasound synovitis in rheumatoid arthritis: a EULAR-OMERACT ultrasound taskforce-Part 1: definition and development of a standardized, consensus-based scoring system. RMD Open. 2017;3(1):e000428.[2]Van den Berg R et al. What is the value of musculoskeletal ultrasound in patients presenting with arthralgia to predict inflammatory arthritis development? A systematic literature review. Arthritis Research & Therapy (2018) 20:228.Disclosure of Interests:None declared

The role of exudation in chronic subdural hematomas

2007 ◽  
Vol 107 (2) ◽  
pp. 290-295 ◽  
Author(s):  
Mehmet Tokmak ◽  
A. Celal Iplikcioglu ◽  
Sirzat Bek ◽  
Cem Atilla Gökduman ◽  
Mustafa Erdal
Keyword(s):  
Outer Membrane ◽  
Clinical Status ◽  
Ct Scans ◽  
Subdural Hematomas ◽  
The Mean ◽  
Grade 3 ◽  
Age Range ◽  
Exudation Rate

Object Chronic subdural hematomas (SDHs) are a local inflammatory process that causes the formation of a granulation tissue often referred to as the external or outer membrane. This membrane has abnormally permeable macrocapillaries. Therefore, exudation from the macrocapillaries in the outer membrane of chronic SDH may play an important role in the enlargement of chronic SDH. In this study the authors investigated the role of exudation in chronic SDH. Methods The authors examined 24 patients (16 men and eight women; age range 38–86 years [mean age 61.4 years]) with 27 chronic SDHs. The clinical status of the patients was evaluated according to the classification described by Markwalder. The diagnosis was established on computed tomography (CT) scans in all cases. The authors also used the Nomura Classification for judging the lesion's appearance on CT scans. Immediately after the diagnosis, all patients were administered 20 mCi (740 mBq) technetium-99m human serum albumin. Four hours later, blood and SDH samples were taken and radioactivity levels were measured in each. The ratio of activity of the samples taken from chronic SDH to the radioactivity of blood was determined as a percentage and defined as the exudation rate. On the follow-up CT scan obtained on postoperative Day 20, subdural collections thicker than 5 mm were determined to be a reaccumulation. Results The correlations between the exudation rate and age of the patients, clinical grades, CT appearances, and amount of reaccumulation were investigated. In this series the average exudation rate was 13.24% (range 2.05–28.88%). The mean exudation rates according to the clinical grades assigned to patients were as follows: Grade 0, 8.67 ± 5.64% (three patients); Grade 1, 5.07 ± 1.43% (eight patients); Grade 2, 17.87 ± 3.73% (seven patients); and Grade 3, 19.65 ± 7.67% (six patients). Exudation rates in patients with Grades 2 and 3 were significantly higher than those in Grades 0 and 1 (p < 0.05). The mean exudation rates according to the lesion's appearance on CT scans were found as follows: hypodense appearance, 6.55 ± 4.52% (eight patients); isodense appearance, 11.07 ± 6.32% (five patients); hyperdense appearance, 19.47 ± 13.61% (three patients); and mixed-density appearance, 17.40 ± 5.80% (nine patients). The differences among the groups were significant (p < 0.05). The average exudation rate was statistically higher in the patients with reaccumulation (16.30 ± 8.16%) than that in the patients without reaccumulation (9.96 ± 6.84%) (p < 0.05). Conclusions The exudation rate in chronic SDH is correlated with a higher clinical grade (Markwalder Grade 2 or 3), mixed-density CT appearance, and reaccumulation. Therefore, exudation from macrocapillaries in the outer membrane of chronic SDH probably plays an important role in the pathophysiology and the growth of chronic SDH.

scholarly journals Bleeding during laparoscopic partial nephrectomy: Can a hemostatic matrix help to improve hemostasis?

2016 ◽  
Vol 88 (3) ◽  
pp. 228 ◽  
Author(s):  
Faruk Ozgor ◽  
Abdulmuttalip Simsek ◽  
Ozgu Aydogdu ◽  
Onur Kucuktopcu ◽  
Omer Sarilar ◽  
...  
Keyword(s):  
Partial Nephrectomy ◽  
Tumor Size ◽  
Operation Time ◽  
Demographic Characteristics ◽  
Ischemia Time ◽  
Nephrometry Score ◽  
The Mean ◽  
Group 1

Objectives: To evaluate the possible role of an hemostatic matrix on hemostasis, perioperative outcomes and complications in patients who underwent laparoscopic partial nephrectomy (LPN). Materials and methods: Patients charts were analyzed retrospectively and their demographic characteristics, operative parameters and follow-up results were recorded. Patients were divided into two groups, according to those who used an hemostatic matrix as Group 1 (n = 41) and those who did not used as Group 2 (n = 44). Demographic characteristics of patients, tumor features, operation time, clamping of the renal vessels, ischemia time, suturing of the collecting system, perioperative hemorrhage and complications were evaluated. Histopathological results, surgical margin status, creatinine level and recurrence at the 3rd month of follow up were analyzed. Statistical analyses were performed with SPSS 17.0 and significance was set at p value of &lt; 0.05. Results: The mean RENAL nephrometry score was 5.9 ± 2.0 and the mean tumor size was 35 ± 12 mm. All patients had a single tumor and 44 of them had a tumor in the right kidney. The renal artery was clamped in 79 cases and the mean ischemia time was 20.1 ± 7 minutes. The mean tumor size and the mean RENAL nephrometry score was statistically higher in Group 1 (p: 0.016 and p &lt; 0.001, respectively). Pelvicaliceal repair was more common in Group 1 due to deeper extension of tumors in this group (p: 0.038). In Group 1, less hemorrhage and blood transfusion requirement, with shorter ischemia and operation time was detected. Conclusion: The outcomes of the recent study showed that adjunctive use of an hemostatic matrix improves hemostasis and decreases hemorrhagic complications during LPN. Further prospective studies are required to assess the potential role of an hemostatic matrix in LPN.

A Successful Application of the Intraoperative Parathyroid Hormone Assay in Tertiary Hyperparathyroidism

2007 ◽  
Vol 73 (3) ◽  
pp. 281-283 ◽  
Author(s):  
Leila Thanasoulis ◽  
Juliane Bingener ◽  
Kenneth Sirinek ◽  
Melanie Richards
Keyword(s):  
Parathyroid Hormone ◽  
Success Rates ◽  
Tertiary Hyperparathyroidism ◽  
Equivalent Rate ◽  
Parathyroid Hormone Assay ◽  
The Mean ◽  
Intraoperative Parathyroid Hormone ◽  
Intraoperative Parathyroid Hormone Assay

The role of the intraoperative parathyroid hormone (IOPTH) assay in patients with tertiary hyperparathyroidism (3HPT) is not well defined. To evaluate the utility of the IOPTH in 3HPT, we compared its use in 72 patients with primary hyperparathyroidism (1HPT) and 3HPT undergoing parathyroidectomy. Sixty-three patients with 1HPT and nine patients with 3HPT were identified. There were 30 men and 42 women (mean age, 58 years). The mean serum calcium and preoperative intact PTH levels in 1HPT were 11.1 mg/dL and 214 pg/mL compared with 11.2 mg/dL and 849 pg/mL in 3HPT (Ca, non significant; PTH, P < 0.05). Intraoperatively, a solitary abnormal gland was found in 62 of 72 (86%) patients. Seven patients with 3HPT had three- or four-gland hyperplasia. The two groups were compared to determine if a 10-minute postexcision IOPTH decline >50 per cent would have similar success rates. Seventy-one of 72 (98.6%) patients had a >50 per cent decline from the baseline IOPTH at the end of the operation. The average reduction from baseline was 85.3 per cent in 1HPT and 88.6 per cent in 3HPT (not significant). Average follow-up was 9.8 months for 1HPT and 11.1 months in 3HPT. Three of 63 patients (4.8%) with 1HPT and five of nine patients (55.6%) with 3HPT had inappropriate elevations in PTH ( P < 0.05). All patients with 3HPT were normocalcemic compared with 62 of 64 (97%) patients with 1HPT (not significant). The IOPTH assay can be used in 3HPT in an identical fashion with an equivalent rate of normocalcemia compared with its applications in 1HPT.

Sign in / Sign up

Export Citation Format

Share Document