Abrams, J.
The Massachusetts Turnpike Authority (turnpike authority) has provided by regulation that a tandem tractor trailer,2 using the Massachusetts Turnpike “may not exceed a total maximum gross weight of 127,400 pounds.” 730 Code Mass. Regs. 4.02 (1978).3 The defendants are charged with operating their tandem tractor trailers at gross weights in excess of 127,400 pounds. At a hearing in the District Court, the defendants filed a motion to dismiss the complaints claiming that 730 Code Mass. Regs. 4.02 (1978) violated equal protection and due process guaranties as well as the commerce clause of the United States Constitution. After an extensive hearing, the judge concluded that the regulation was unconstitutional on equal protection grounds, and he dismissed the complaints. The Commonwealth appealed, see Mass. R. Crim. P. 15 (a) (1), 378 Mass. 882 (1979), and we granted the parties’ joint application for direct appellate review. We reverse and remand the cases for trial.
We summarize the facts. The defendants are interstate common carriers, operating tandem trailer trucks. The Massachusetts Turnpike is the only State highway in Massachusetts on which tandem tractor trailers are allowed. But see Surface Transportation Assistance Act of 1982, Pub. [801]*801L. No. 97-424 (March 23, 1983). For purposes of the motion, the parties stipulated that all the vehicles cited exceeded the regulation’s gross weight limitations. The parties also stipulated that “[t]he primary purpose of the administrative regulations, pursuant to which the complaints issued, is to preserve the integrity and safety of bridges under the control” of the turnpike authority.4
In 1980, the turnpike authority amended its regulation, 730 Code Mass. Regs. 5.06, pertaining to single tractor trailer units by increasing the gross load allowance for units with four or more axles from 73,000 pounds to 80,000, and established a “reducible load” system, which enabled owners of vehicles with five or more axles to purchase a card annually authorizing them to carry 99,000 pounds. The regulation was amended in order to bring turnpike weight limitations for single tractor trailers in line with those established by the Department of Public Works for like vehicles on State roads.5 No proportionate increases were made for tandem tractor trailer units using the turnpike.
The judge found that in 1977 engineers for the New York State Thruway prepared a report on “Gross Weights and [802]*802Axle Configurations for Tandem Operations.” As a result of this report, the New York State Thruway concluded that it could safely increase the tandem tractor trailer gross weight limitations from 127,400 to 143,000 pounds. The New York study was based on a modification of the standard 1944 and 1953 American Association of State Highway Officials (AASHO) Specifications for Highway Bridges.
There are approximately 180 bridges maintained by the turnpike authority. The majority of the 180 bridges on the turnpike were constructed in the 1950’s in conformity with the 1944 and 1953 AASHO’s specifications. Five percent of the bridges are long enough to allow an entire tandem tractor trailer on the bridge at one time. The judge concluded that since 95% of the turnpike bridges were less than 150 feet in length and thus would not need to support the entire length of the tandem tractor trailer on the bridge at once, the gross weight limit could be increased to 143,000 pounds in conformity with the 1977 AASHO specifications. The judge also concluded that regulation 4.02, restricting the gross weight of tandem tractor trailers to a maximum of 127,400 pounds was “without reasonable relation to the impact [of tandem trailers] on such bridges,” and therefore the “complaints violate the equal protection provisions of the Federal and Massachusetts Constitutions.”6
1. Equal protection challenge to 730 Code Mass. Regs. 4.02 (1978). At the hearing, the defendants offered evidence that on many turnpike bridges a single tractor trailer unit with five or more axles, loaded to the gross 99,000 pound limit, creates stress significantly in excess of that allowed under the tandem tractor trailer gross weight and axle weight limitations. The Commonwealth, however, offered evidence that at least as to one long-span bridge, the 99,000 pound permit vehicle overstressed that [803]*803bridge by 5%, and that the tandem tractor trailer, with a gross weight of 127,400 pounds, overstressed that bridge by 9 %. Experts for the Commonwealth believed that increasing the gross weight limit for tandem tractor trailers using the turnpike would adversely affect long-span bridges. Further, high axle loads, such as a 99,000 pound permit vehicle, primarily damage bridge decks or the pavement over a bridge, while high gross weights could damage the bridge supports. There was evidence that, from an engineering standpoint, the greater weight of the tandems induces more stress in long-span bridges, and therefore it was rational to differentiate between the gross weight limit on single and tandem trailers.
Nevertheless, the judge found that 95% of the bridges on the turnpike would fall well within the acceptable range of stress even if tandems were permitted to increase their maximum gross weights to 143,000 pounds. Therefore, he concluded that regulation 4.02, limiting tandem trailers’ maximum gross weight to 127,400 pounds, did not bear a reasonable relation to the impact on the turnpike bridges. We do not agree.
We start with the fundamental principle that regulations promulgated pursuant to statutory authority have a presumption of constitutionality, see Consolidated Cigar Corp. v. Department of Pub. Health, 372 Mass. 844, 851 (1977), and are treated by the court with the same deference as a statutory enactment, Massachusetts State Pharmaceutical Ass’n v. Rate Setting Comm’n, 387 Mass. 122, 127 (1982); Greenleaf Fin. Co. v. Small Loans Regulatory Bd., 377 Mass. 282, 293 (1979). Further, in ruling on the defendants’ equal protection claim, our duty is to determine “whether the classification made by the regulation rationally furthers a legitimate State purpose.” Commonwealth v. Petralia, 372 Mass. 452, 455 (1977). “The weight of the evidence [is] for the [agency], not the courts.” Shell Oil Co. v. Revere, 383 Mass. 682, 689 (1981). “Although persons challenging the constitutionality of [the regulation] may introduce evidence in support of their claim that the [class[804]*804ification] is irrational, . . . they will not prevail if ‘the question [of the classification’s rationality] is at least debatable’ in view of the evidence [before the judge].” Id. at 688, quoting United States v. Carotene Prods. Co., 304 U.S. 144, 153-154 (1938). See Zayre Corp. v. Attorney Gen., 372 Mass. 423, 432 (1977).
Since the Commonwealth offered some evidence in support of its regulation, it was at least debatable whether tandem units with gross weights in excess of 127,400 pounds place excessive stress on the turnpike’s long-span bridges. Because the issue was “at least debatable,” the classification between single and tandem tractor trailers is not unconstitutional by reason of violating equal protection principles . “ [I]t is only the invidious discrimination, the wholly arbitrary act, which cannot stand consistently with the Fourteenth Amendment.” Klein v.
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Abrams, J.
The Massachusetts Turnpike Authority (turnpike authority) has provided by regulation that a tandem tractor trailer,2 using the Massachusetts Turnpike “may not exceed a total maximum gross weight of 127,400 pounds.” 730 Code Mass. Regs. 4.02 (1978).3 The defendants are charged with operating their tandem tractor trailers at gross weights in excess of 127,400 pounds. At a hearing in the District Court, the defendants filed a motion to dismiss the complaints claiming that 730 Code Mass. Regs. 4.02 (1978) violated equal protection and due process guaranties as well as the commerce clause of the United States Constitution. After an extensive hearing, the judge concluded that the regulation was unconstitutional on equal protection grounds, and he dismissed the complaints. The Commonwealth appealed, see Mass. R. Crim. P. 15 (a) (1), 378 Mass. 882 (1979), and we granted the parties’ joint application for direct appellate review. We reverse and remand the cases for trial.
We summarize the facts. The defendants are interstate common carriers, operating tandem trailer trucks. The Massachusetts Turnpike is the only State highway in Massachusetts on which tandem tractor trailers are allowed. But see Surface Transportation Assistance Act of 1982, Pub. [801]*801L. No. 97-424 (March 23, 1983). For purposes of the motion, the parties stipulated that all the vehicles cited exceeded the regulation’s gross weight limitations. The parties also stipulated that “[t]he primary purpose of the administrative regulations, pursuant to which the complaints issued, is to preserve the integrity and safety of bridges under the control” of the turnpike authority.4
In 1980, the turnpike authority amended its regulation, 730 Code Mass. Regs. 5.06, pertaining to single tractor trailer units by increasing the gross load allowance for units with four or more axles from 73,000 pounds to 80,000, and established a “reducible load” system, which enabled owners of vehicles with five or more axles to purchase a card annually authorizing them to carry 99,000 pounds. The regulation was amended in order to bring turnpike weight limitations for single tractor trailers in line with those established by the Department of Public Works for like vehicles on State roads.5 No proportionate increases were made for tandem tractor trailer units using the turnpike.
The judge found that in 1977 engineers for the New York State Thruway prepared a report on “Gross Weights and [802]*802Axle Configurations for Tandem Operations.” As a result of this report, the New York State Thruway concluded that it could safely increase the tandem tractor trailer gross weight limitations from 127,400 to 143,000 pounds. The New York study was based on a modification of the standard 1944 and 1953 American Association of State Highway Officials (AASHO) Specifications for Highway Bridges.
There are approximately 180 bridges maintained by the turnpike authority. The majority of the 180 bridges on the turnpike were constructed in the 1950’s in conformity with the 1944 and 1953 AASHO’s specifications. Five percent of the bridges are long enough to allow an entire tandem tractor trailer on the bridge at one time. The judge concluded that since 95% of the turnpike bridges were less than 150 feet in length and thus would not need to support the entire length of the tandem tractor trailer on the bridge at once, the gross weight limit could be increased to 143,000 pounds in conformity with the 1977 AASHO specifications. The judge also concluded that regulation 4.02, restricting the gross weight of tandem tractor trailers to a maximum of 127,400 pounds was “without reasonable relation to the impact [of tandem trailers] on such bridges,” and therefore the “complaints violate the equal protection provisions of the Federal and Massachusetts Constitutions.”6
1. Equal protection challenge to 730 Code Mass. Regs. 4.02 (1978). At the hearing, the defendants offered evidence that on many turnpike bridges a single tractor trailer unit with five or more axles, loaded to the gross 99,000 pound limit, creates stress significantly in excess of that allowed under the tandem tractor trailer gross weight and axle weight limitations. The Commonwealth, however, offered evidence that at least as to one long-span bridge, the 99,000 pound permit vehicle overstressed that [803]*803bridge by 5%, and that the tandem tractor trailer, with a gross weight of 127,400 pounds, overstressed that bridge by 9 %. Experts for the Commonwealth believed that increasing the gross weight limit for tandem tractor trailers using the turnpike would adversely affect long-span bridges. Further, high axle loads, such as a 99,000 pound permit vehicle, primarily damage bridge decks or the pavement over a bridge, while high gross weights could damage the bridge supports. There was evidence that, from an engineering standpoint, the greater weight of the tandems induces more stress in long-span bridges, and therefore it was rational to differentiate between the gross weight limit on single and tandem trailers.
Nevertheless, the judge found that 95% of the bridges on the turnpike would fall well within the acceptable range of stress even if tandems were permitted to increase their maximum gross weights to 143,000 pounds. Therefore, he concluded that regulation 4.02, limiting tandem trailers’ maximum gross weight to 127,400 pounds, did not bear a reasonable relation to the impact on the turnpike bridges. We do not agree.
We start with the fundamental principle that regulations promulgated pursuant to statutory authority have a presumption of constitutionality, see Consolidated Cigar Corp. v. Department of Pub. Health, 372 Mass. 844, 851 (1977), and are treated by the court with the same deference as a statutory enactment, Massachusetts State Pharmaceutical Ass’n v. Rate Setting Comm’n, 387 Mass. 122, 127 (1982); Greenleaf Fin. Co. v. Small Loans Regulatory Bd., 377 Mass. 282, 293 (1979). Further, in ruling on the defendants’ equal protection claim, our duty is to determine “whether the classification made by the regulation rationally furthers a legitimate State purpose.” Commonwealth v. Petralia, 372 Mass. 452, 455 (1977). “The weight of the evidence [is] for the [agency], not the courts.” Shell Oil Co. v. Revere, 383 Mass. 682, 689 (1981). “Although persons challenging the constitutionality of [the regulation] may introduce evidence in support of their claim that the [class[804]*804ification] is irrational, . . . they will not prevail if ‘the question [of the classification’s rationality] is at least debatable’ in view of the evidence [before the judge].” Id. at 688, quoting United States v. Carotene Prods. Co., 304 U.S. 144, 153-154 (1938). See Zayre Corp. v. Attorney Gen., 372 Mass. 423, 432 (1977).
Since the Commonwealth offered some evidence in support of its regulation, it was at least debatable whether tandem units with gross weights in excess of 127,400 pounds place excessive stress on the turnpike’s long-span bridges. Because the issue was “at least debatable,” the classification between single and tandem tractor trailers is not unconstitutional by reason of violating equal protection principles . “ [I]t is only the invidious discrimination, the wholly arbitrary act, which cannot stand consistently with the Fourteenth Amendment.” Klein v. Catalano, 386 Mass. 701, 717 (1982), quoting New Orleans v. Dukes, 427 U.S. 297, 303-304 (1976). “[R]ough accommodations that to some extent result in dissimilarity of treatment” are permissible unless the classifications are arbitrary or irrational. Commonwealth v. Henry’s Drywall Co., 366 Mass. 539, 545 (1974). “Whether [the regulation is] wise or effective is not, of course, the province of [courts].” Klein v. Catalano, supra at 707, quoting Hoffman Estates v. Flipside Hoffman Estates, Inc., 455 U.S. 489, 505 (1982). Commonwealth v. Lammi, 386 Mass. 299, 300 (1982). Since the turnpike authority’s regulation is supported by evidence that it preserves the safety and integrity of the turnpike bridges, the regulation bears a reasonable relation to its goal, and the defendants’ equal protection claim fails. Grocery Mfrs. of America, Inc. v. Department of Pub. Health, 379 Mass. 70, 85 (1979).
2. Due process claim. The defendants assert that the 127,400 pound gross weight limitation is “without logic or rationality.” The defendants also claim that axle weight limitations would be the “least restrictive means” and therefore a more appropriate weight regulation. They claim that axle weight limitations would be equally effective in [805]*805preserving the turnpike bridges. The defendants also assert that the regulation is unconstitutionally vague.
In order to survive a due process challenge, the purpose of 730 Code Mass. Regs. 4.02 (1978) “must be rationally related to the promotion of public safety . . . [and] the means chosen to effectuate the legislative purpose must be reasonable.” Consolidated Cigar Corp. v. Department of Pub. Health, 372 Mass. 844, 851 (1977). Shell Oil Co. v. Revere, 383 Mass. 682, 686 (1981). Commonwealth v. Henry’s Drywall Co., 366 Mass. 539, 543 (1974). Contrary to the defendants’ assertions, the Commonwealth has demonstrated that the regulation is not arbitrary but is rationally related to the purpose of preventing excessive stress on the turnpike’s long-span bridges. The fact that the tandem gross weight limitation is not drawn with “mathematical precision,” or that a better means of protection might be available or that the regulation “is not perfectly consistent with the desired result” is not fatal. Shell Oil Co. v. Revere, supra at 687. The turnpike authority need not guarantee success when it chooses to regulate for the public safety. Id.
The defendants also argue that regulation 4.02 violates due process principles because the axle weight limitations contained within the regulation are the “least restrictive means” to achieve the purposes of the regulation, and that these axle weight limitations would be equally effective in advancing the object of preserving the turnpike bridges. Since we have concluded that the Commonwealth has shown the “necessary nexus” between the regulation and its avowed purpose of preserving turnpike bridge integrity, see Blue Hills Cemetery, Inc. v. Board of Registration in Embalming & Funeral Directing, 379 Mass. 368, 375 n.11 (1979), the turnpike authority has met its burden. The resolution of conflicting evidence is for the turnpike authority, not the courts. Borden, Inc. v. Commissioner of Pub. Health, ante 707, 723 (1983). Courts do not substitute their judgment for that of the agency nor do they assess the effectiveness of alternative means. Blue Hills Cemetery, Inc., v. Board of Registration in Embalming & Funeral Directing, supra at 375.
[806]*806Finally, the defendants assert that regulation 4.02 is unreasonably vague because it contains a gross weight limitation, a formula limiting weight of the tractor and first trailer unit, and an axle weight limitation. We assume that a “regulation whose violation is a criminal act is tested by a higher standard of definiteness than a noncriminal regulation.” Grocery Mfrs. of America, Inc. v. Department of Pub. Health, 379 Mass. 70, 83 (1979). “[C]riminal conduct must be delineated with a reasonable degree of definiteness ... [so that] those who may be subject to its penalties should not be forced to guess at its meaning.” Opinions of the Justices, 378 Mass. 822, 827 (1979). A criminal statute will be treated as void for vagueness if it “fails to give a person of ordinary intelligence fair notice that his contemplated action is forbidden.” Grocery Mfrs. of America, Inc. v. Department of Pub. Health, supra at 84.
Every tandem tractor trailer owner and operator is clearly put on notice that “[a]ny such combinations of vehicles may not exceed a total maximum gross weight of 127,400 pounds.” 730 Code Mass. Regs. 4.02. The regulation is very clear that trucks with gross weights in excess of the 127,400 pound limitation are forbidden. Therefore, we conclude that regulation 4.02 is not unconstitutionally vague.
3. The restraints of the commerce clause. The defendants argue that regulation 4.02 violates the commerce clause of the United States Constitution. U.S. Const, art. 1, § 8, cl. 3. The defendants do not dispute that the Commonwealth has a legitimate interest in regulating truck weights to foster highway safety by preserving bridge and road surface structures. Nor do they contend that Federal legislation has preempted the Commonwealth’s regulation of State tandem tractor trailer weights.7 Rather, the companies [807]*807argue that the regulation excessively burdens interstate commerce in relation to the asserted local benefits. Raymond Motor Transp., Inc. v. Rice, 434 U.S. 429, 442 (1978). The companies contend that the Commonwealth’s evidence did not show that the regulation contributed to highway safety but, rather, that the companies demonstrated that the regulation would impose a substantial burden on interstate commerce in terms of expense and delay. We do not agree.
While the commerce clause, even without congressional action, is a limitation on State power, and “prevents the States from erecting barriers to the free flow of interstate commerce,” Raymond Motor Transp., Inc. v. Rice, 434 U.S. 429, 440 (1978), it does not invalidate all State restrictions on commerce. Kassel v. Consolidated Freightways Corp., 450 U.S. 662, 669 (1981). “[I]n the absence of conflicting legislation by Congress, there is a residuum of power in the state to make laws governing matters of local concern which nevertheless in some measure affect interstate commerce.” Southern Pac. Co. v. Arizona, 325 U.S. 761, 767 (1945).
The State’s power to regulate commerce is the greatest when it regulates matters traditionally considered to be of local concern. Hunt v. Washington State Apple Advertising Comm’n, 432 U.S. 333, 350 (1977). “[Regulations that touch upon safety — especially highway safety — are those that ‘the Court has been most reluctant to invalidate.’” Kassel v. Consolidated Freightways Corp. of Del., 450 U.S. 662, 670 (1981), quoting Raymond Motor Transp., Inc. v. Rice, 434 U.S. 429, 443 (1978).8 See South Carolina State Highway Dep’t v. RarnwellBros., 303 U.S. 177,187 (1938).
[808]*808Since there is no dispute that regulation of truck weights to promote highway safety is a legitimate State interest, we examine 730 Code Mass. Regs. 4.02 (1978) to determine whether it is a safety regulation designed to “effectuate a legitimate local public interest,” and whether it imposes an impermissible burden on interstate commerce. Pike v. Bruce Church, Inc., 397 U.S. 137,142 (1970). See Kassel v. Consolidated Freightways Corp., 450 U.S. 662, 670-671 (1981). The “regulation does not discriminate between instate and out-of-State businesses.” Grocery Mfrs. of America, Inc. v. Department of Pub. Health, 379 Mass. 70, 80 (1979). Raymond Motor Transp., Inc. v. Rice, 434 U.S. 429, 444 n. 18 (1978). Unlike Iowa in Kassel, and Wisconsin in Raymond, the Commonwealth has presented expert evidence that tandem tractor trailers weighing in excess of 127,400 pounds place excessive stress on long-span turnpike bridges. Kassel v. Consolidated Freightways Corp., supra at 671. Raymond Motor Transp., Inc. v. Rice, supra at 444-445.
Moreover, while at the time the complaints were issued against the defendants, New York allowed tandem tractor trailers with gross weights of 143,000 pounds to operate on the New York State Thruway, evidence before the District Court showed that Maine, Connecticut, New Jersey, and Pennsylvania did not allow any tandem tractor trailers to operate on their highways or turnpikes.9 Thus, the Commonwealth is not “out-of-step” with surrounding States. Cf. Kassel, supra at 675-678. Finally, at the time of these violations, there was no conflict between 730 Code Mass. Regs. 4.02 (1978) and Federal standards. Cf. Surface Transportation Assistance Act of 1982, Pub. L. No. 97-424 (March 23, 1983).
The only possible burden on interstate commerce raised by the defendants is that Massachusetts requires tandem [809]*809tractor trailers to operate with a lower weight on its turnpike than New York authorizes on its Thruway. This difference results in some increase in expense and time only if tandem trailers operating exclusively between New York and Massachusetts choose to carry the 143,000 pound weight permitted by New York, rather than the 127,400 pound weight permitted by Massachusetts, and must be separated into single trailers or otherwise reloaded to conform to Massachusetts weight limitations. While increased time and expense are factors to be considered in determining the extent of a regulation’s burden on interstate commerce, Raymond Motor Transp., Inc. v. Rice, 434 U.S. 429, 445 (1978), the defendants failed to show that such costs or delays were a significant burden on interstate commerce.10 Cf. Grocery Mfrs. of America, Inc. v. Department of Pub. Health, 379 Mass. 70 (1979); Kassel v. Consolidated Freightways Corp., 450 U.S. 662 (1981). On the record, there is no showing that the regulation discriminates against or substantially burdens interstate commerce.
Consequently, we hold that 730 Code Mass. Regs. 4.02 (1978) does not violate equal protection, due process, or the commerce clause principles. We vacate the order dismissing the complaints against the defendants and remand the cases for trial.
So ordered.