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

Joseph Abate, Ward Whitt
1997 Operations Research Letters  
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.  ...  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.  ... 
doi:10.1016/s0167-6377(97)00016-3 fatcat:ez6fyopq6ra63ldohkcfctr4xi

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

Esa Hyytiä, Samuli Aalto, Aleksi Penttinen
2012 Proceedings of the 12th ACM SIGMETRICS/PERFORMANCE joint international conference on Measurement and Modeling of Computer Systems - SIGMETRICS '12  
functions 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.  ... 
doi:10.1145/2254756.2254763 dblp:conf/sigmetrics/HyytiaAP12 fatcat:6g3wum3rcbfopaiy52v53r2jym

Minimizing Slowdown in Heterogeneous Size-Aware Dispatching Systems (full version) [article]

Esa Hyytiä, Samuli Aalto, Aleksi Penttinen
2012 arXiv   pre-print
functions 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.  ... 
arXiv:1203.5040v1 fatcat:kr5d3yjw7bbuzaaibwidmlr74e

Minimizing slowdown in heterogeneous size-aware dispatching systems

Esa Hyytiä, Samuli Aalto, Aleksi Penttinen
2012 Performance Evaluation Review  
functions 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.  ... 
doi:10.1145/2318857.2254763 fatcat:mx43mv6lvjge5fkhpuffcgdnfa

Size- and state-aware dispatching problem with queue-specific job sizes

Esa Hyytiä, Aleksi Penttinen, Samuli Aalto
2012 European Journal of Operational Research  
First we derive 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).  ... 
doi:10.1016/j.ejor.2011.09.029 fatcat:xojtsay2cfb2jmefbsyjahup5m

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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