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Limits and approximations for the M/G/1 LIFO waiting-time distribution

1997
*
Operations Research Letters
*

We provide additional descriptions of

doi:10.1016/s0167-6377(97)00016-3
fatcat:ez6fyopq6ra63ldohkcfctr4xi
*the*steady-state*waiting*-*time**distribution*in*the**M*/*G*/*1*queue with*the*last-in first-out (*LIFO*) service discipline. ... We establish heavy-traffic*limits**for*both*the*cumulative*distribution*function (cdf)*and**the*moments. ... We start in Section 2 by establishing a heavy-traffic*limit*theorem*for**the**M*/*G*/*1**LIFO*steadystate*waiting*-*time**distribution*. ...##
###
Page 4476 of Mathematical Reviews Vol. , Issue 93h
[page]

1993
*
Mathematical Reviews
*

These relationships hold over a class of queueing models that include

*M*/*G*/*1*\ queues with exceptional first service,*M*/*G*/*1*queues with server vacations,*and**M*/*G*/*1*priority models. ...*The**M*/*G*/*1*queue with batch arrivals is studied.*The*queueing discipline is a generalisation of processor sharing. ...##
###
Page 6493 of Mathematical Reviews Vol. , Issue 87k
[page]

1987
*
Mathematical Reviews
*

*The*authors are able to interpret this result by using remaining-work arguments connect- ing

*the*classical

*M*/

*G*/

*1*/

*LIFO*with

*the*

*M*/

*G*/

*1*/

*LIFO*preemptive- resume queue. Carl M. ...

*The*fact that

*the*equilibrium system

*waiting*-

*time*

*distribution*of

*the*

*M*/

*G*/

*1*queue can be written as a geometric mixture of convo- lutions of

*the*residual-service-

*time*cumulative

*distribution*func- tion ...

##
###
Page 415 of Mathematical Reviews Vol. , Issue 98A
[page]

1998
*
Mathematical Reviews
*

*M*/

*G*/

*1*|

*LIFO*

*waiting*-

*time*

*distribution*. ... Summary: “We provide additional descriptions of

*the*steady-state

*waiting*-

*time*

*distribution*in

*the*

*M*/

*G*/

*1*queue with

*the*last-in first- out (

*LIFO*) service discipline. ...

##
###
Minimizing slowdown in heterogeneous size-aware dispatching systems

2012
*
Proceedings of the 12th ACM SIGMETRICS/PERFORMANCE joint international conference on Measurement and Modeling of Computer Systems - SIGMETRICS '12
*

functions

doi:10.1145/2254756.2254763
dblp:conf/sigmetrics/HyytiaAP12
fatcat:6g3wum3rcbfopaiy52v53r2jym
*for**M*/*G*/*1*-FIFO/*LIFO*/SPTP/SPT/SRPT with general holding costs of which*the*slowdown criterion is a special case;*and*3) to utilize*the*value functions to derive efficient dispatching policies ... We are interested in minimizing*the*so-called mean slowdown criterion corresponding to*the*mean of*the*sojourn*time*divided by*the*processing*time*. ... Corollary 2: Consider an*M*/*G*/*1*queue*for*which*the*support of*the*service*time**distribution*is finite. ...##
###
Minimizing Slowdown in Heterogeneous Size-Aware Dispatching Systems (full version)
[article]

2012
*
arXiv
*
pre-print

functions

arXiv:1203.5040v1
fatcat:kr5d3yjw7bbuzaaibwidmlr74e
*for**M*/*G*/*1*-FIFO/*LIFO*/SPTP/SPT/SRPT with general holding costs of which*the*slowdown criterion is a special case;*and*3) to utilize*the*value functions to derive efficient dispatching policies ... We are interested in minimizing*the*so-called mean slowdown criterion corresponding to*the*mean of*the*sojourn*time*divided by*the*processing*time*. ... Corollary 2: Consider an*M*/*G*/*1*queue*for*which*the*support of*the*service*time**distribution*is finite. ...##
###
Minimizing slowdown in heterogeneous size-aware dispatching systems

2012
*
Performance Evaluation Review
*

functions

doi:10.1145/2318857.2254763
fatcat:mx43mv6lvjge5fkhpuffcgdnfa
*for**M*/*G*/*1*-FIFO/*LIFO*/SPTP/SPT/SRPT with general holding costs of which*the*slowdown criterion is a special case;*and*3) to utilize*the*value functions to derive efficient dispatching policies ... We are interested in minimizing*the*so-called mean slowdown criterion corresponding to*the*mean of*the*sojourn*time*divided by*the*processing*time*. ... Corollary 2: Consider an*M*/*G*/*1*queue*for*which*the*support of*the*service*time**distribution*is finite. ...##
###
Size- and state-aware dispatching problem with queue-specific job sizes

2012
*
European Journal of Operational Research
*

First we derive

doi:10.1016/j.ejor.2011.09.029
fatcat:xojtsay2cfb2jmefbsyjahup5m
*the*so-called size-aware relative values of states with respect to*the*sojourn*time*in an*M*/*G*/*1*queue operating under FIFO,*LIFO*, SPT or SRPT disciplines. ...*For*FIFO*and**LIFO*,*the*size-aware relative values turn out to be insensitive to*the*form of*the*job size*distribution*. ... Figure 3 : 3 Difference in*the*cumulative sojourn*times*in*M*/*G*/*1*-FIFO between a system in state z*and*an empty system.Proposition 3.1 (*M*/*G*/*1*-FIFO). ...##
###
Page 6999 of Mathematical Reviews Vol. , Issue 99j
[page]

1999
*
Mathematical Reviews
*

customer servicing

*time*(length),*and*a*limited*number of*waiting*places. ... (RS-MTEC; Moscow)*The*system*M*;/*G*/*1*/n with*the**LIFO*discipline*and*a constraint on*the*total number of customers. (Russian. Russian summary) Avtomat. i Telemekh. 1998, no. 4, 106-116. ...##
###
Page 3500 of Mathematical Reviews Vol. , Issue 82h
[page]

1982
*
Mathematical Reviews
*

Author’s summary: “An

*M*/*G*/*1*queueing system is studied in which*the*service*time*required by a customer is dependent on*the*interarrival*time*between his arrival*and*that of his predecessor. ... Assuming*the*two variables are ‘associated’, we prove that*the*expected delay in this system is less than or equal to that of a conventional*M*/*G*/*1*queue. ...##
###
Page 1847 of Mathematical Reviews Vol. 55, Issue 6
[page]

1978
*
Mathematical Reviews
*

Consider an

*M*/*G*/*1*queue with several types of customers, where a type i customer has an expected service*time*»,*and*a holding cost per unit*time*c;. ...*The*author proves two results:*for*an*M*/*G*/*1*queue (1+ ,)~*(1—p,)< var W,/var Wa<1—p,,*and**for*a G/M/m queue var W,/var W.=O(1 — pa). {*For**the*entire collection see MR 55 #4316.} M. A. ...##
###
Page 4424 of Mathematical Reviews Vol. , Issue 82j
[page]

1982
*
Mathematical Reviews
*

Po 82j:60171 Joint

*distribution*of virtual*waiting**time*in*M*,|*G*,|*1*|0o systems with relative*and*absolute priority. (Russian) Dokl. Akad. Nauk UzSSR 1981, no. 1, 11-13. ... Dimitrov (Sofia) Husanov, M. 82j:60173 Virtual*waiting**time*in*the*queueing system*M*/*G*/*1*with exponential “‘ warm-up”. (Russian. Uzbek summary) Izv. Akad. Nauk UzSSR Ser. Fiz.-Mat. ...##
###
Page 3776 of Mathematical Reviews Vol. , Issue 98F
[page]

1998
*
Mathematical Reviews
*

They also provide results

*for**the*symmetric batch departure*M*/*G*//*1*queue. ...*The**M**/*G*"/*1*/K queue considered here has a finite*waiting*room of size K.*The*objective is to find*the*probability that an arriving customer is lost. ...##
###
Page 6299 of Mathematical Reviews Vol. , Issue 97J
[page]

1997
*
Mathematical Reviews
*

Summary: “

*The*controlled*M**/*G*/*1*-type queueing model with two modes of operation is considered.*The*modes are characterized by different service*time**distributions**and*arrival rates. ... 6299 initiation*and**the*service completion events.” 97j:60171 60K25 Dudin, Alexander |Dudin, Aleksandr] (BE-BELAMI-PB; Minsk) Optimal control*for*an*M** /*G*/*1*queue with two operation modes. ...##
###
Page 472 of Mathematical Reviews Vol. 58, Issue 1
[page]

1979
*
Mathematical Reviews
*

Using a monotonicity property of G//G/1, he proves that

*the*mean stationary*waiting**time*is greater than that in*M*/*G*/*1*\ with*the*same mean interarrival*time**and**the*same service*time**distribution*. ...*The*author presents functional*limit*theorems that describe*the**limiting**distributions*of w,,*and*W,(t) as n, k, t-»0co. ...
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